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Most of the content of this page is derived from the "Ask Dr. Beetzwaken" column from the Xootr LLC Newsletter.
Ask Dr. Beetzwaken:
Are 406mm bicycle wheels as fast as standard 700C wheels?
What do you think of the Kyoto Protocol?
Why does the use of personal transportation devices seem more prevalent outside the US?
How likely am I to get rained on if I commute by bicycle, scooter, or motorbike?
How much of society's energy consumption is for transportation?
Historically, where did motorcycles come from?
Are there negative environmental impacts associated with human power?
How should personal transporation devices be regulated?
What is wind chill?
How many calories are burned riding a kick scooter?
How much power does it take to move a person on a scooter or cycle?
What is an amp-hour?
What is CNC machining?
What is aircraft aluminum?
Do electric vehicles really use less energy than gas-powered vehicles?
What is regenerative braking?
What are brushless motors?
ARE 406mm BICYCLE WHEELS (i.e., "20 inch") AS FAST AS STANDARD 700C WHEELS?
When riding at constant speed on level ground, the power delivered to the pedals goes three places: (1) friction in the pedals, cranks, chain, and gears; (2) rolling resistance of the tires; and (3) wind resistance (i.e., "air drag") of the bicycle and rider.
For a conventional chain and derailleur drive, the efficiency of the drive system is about 98 percent, and this number doesn't vary much across bikes (except for those with internal hub gears, which are much worse.) So, for simplicity, let's focus on wind resistance and rolling resistance.
The power required to overcome wind resistance increases as the cube (power of three) with speed. So, a doubling of speed results in an eight-fold increase in the power consumed by rolling resistance. The power required to overcome rolling resistance, in contrast, increases in direct proportion to speed, so a doubling of speed results in just a doubling in the power consumed by rolling resistance. This means that as speed increases, wind resistance becomes increasing significant until it consumes a dominant fraction of the rider's power. At speeds over about 15 mph (25 kph), wind resistance matters a lot.
It is true that a 406mm tire will exhibit higher rolling resistance than a 700C ("full size") tire for an equivalent tire and inflation pressure. At first glance this is a nasty penalty to pay for a smaller tire. However, in reality this difference won't matter much for most of us. This is because rolling resistance just isn't a very significant portion of the power requirement in most day-to-day riding situations.
At 15 mph (25 kph) an average rider on a standard "hybrid" bike will have to deliver about 150 watts to the pedals, with almost all of it going to wind resistance. The same rider on a bike with 406mm tires might have to deliver an extra 10-15 watts of power to go 15 mph. However, this amounts to just a few percent of the total power required. In practice, this usually means riding a fraction of a mile per hour more slowly. A much more significant factor is the riding position of the rider (with an upright riding position increasing the power requirement by as much as 25 percent over a crouched riding position).
I've run a lot of experiments over the last year with 406mm tires. The rolling resistance is definitely higher than for 700C tires, as theory predicts. However, this difference is not apparent to the rider except in highly competitive situations at peak power output.
WHAT DO YOU THINK OF THE KYOTO PROTOCOL?
The Kyoto protocol went into effect last week, with relatively little fanfare in the US (the US congress has not ratified the treaty). The basic elements of the protocol are:
1. Member countries agree to reduce their average emissions of carbon dioxide over the period 2008 - 2012.
2. The reduction target is 7 percent below the level of each country's 1990 emissions.
3. If the country can reduce below that target, it earns credits which may be sold. If the country does not reduce its emissions below the target, it must buy credits from other countries to make up the difference.
There is a major flaw in the Kyoto Protocol-- it does not account for the changes in the productive output of the member countries' economies since 1990, the year in which the baseline emissions level is established. This flaw is most clearly manifest in the case of Russia, whose economy has shrunk dramatically since 1990. As a result, Russia's emissions are currently far below the target levels and it may therefore sell its credits. This is a huge windfall for Russia and what several observers have called "selling hot air." The converse would have applied to the US. The US economy grew dramatically since 1990, and so the US is so far from the Kyoto target levels that it would be extraordinarily difficult to meet the targets without suffering a major economic shock.
So, what do I think? I do not think that Kyoto will make a measurable direct difference on global warming. I do think that it is a remarkable milestone in international cooperation around an environmental objective. This is extraordinarily positive. (Incidentally, I think the US should have tried a bit harder to influence the protocol to make it even remotely economically feasible at home.)
I think global warming is one of several potential causes of a demise of our civilization as we know it. (There are a bunch of others, too, including purely "natural" causes and various political or religious causes.) I've recently been reading Jared Diamond's books (Guns, Germs, and Steel; and Collapse), which are truly fascinating accounts of the path of humanity over long time scales. Frankly, if history is a guide, humanity is not likely to continue as we know it now. The question is whether as a global community we wish to influence the path it takes.
WHY DOES THE USE OF PERSONAL TRANSPORTATION DEVICES SEEM MORE PREVALENT OUTSIDE THE US?
Whenever I travel outside the United States, I notice a lot more people seem to be using personal transportation devices than in the US. Is there a rational explanation for this? Another way to phrase this question is "What explains an individual's choice of transportation mode?" There is actually a fairly large body of academic research on this question. I believe that in the long run, on average, individuals tend to make rational choices-- that is, choices that maximize their own well being and satisfaction. In fact, this is the basic assumption that underlies most economic theory.
To explain transportation choices, we need therefore to understand the factors that underlie individual satisfaction with transportation choices. Some of these factors are:
Note that these factors should probably be labeled "perceived factors." For example, actual safety is probably less important than perceived safety.
Cost is an interesting factor. Automobiles have relatively high fixed costs (acquisition, insurance, and depreciation) and relatively low variable costs (actual gasoline consumption per mile, for example). Therefore, once someone has committed to owning an automobile, the marginal cost of driving it an extra mile are pretty low. However, not owning an automobile at all saves thousands of dollars per year, enough to pay for a lot of taxis and car rentals. Many studies have explored the trade-offs consumers are willing to make between cost and time. These are somewhat subtle relationships, but in rough terms, consumers value their time at about one third of their normal wages. That is, a consumer who earns $30 per hour values his or her time at about $10 per hour and would be expected to spend an extra $10 to save an hour in transportation.
I believe that these simple factors are pretty much enough to explain most regional differences in transportation choices. For example, in Italy, acquisition and operation of automobiles is quite expensive, city streets are highly congested, and the weather is mild most of the year. As a result, the motorbike is a prominent mode of transportation. In The Netherlands, the terrain is flat, cities are designed around bicycle paths, and automobiles are relatively expensive. As a result, bicycles are the rational transportation choice for many, many consumers.
A thorny question is to what extent governments and other institutions can influence transportation choices. I believe that there are several significant levers that can be applied. I will not advocate any of them here (although you can probably guess which I might support), but only list the most obvious ones:
1. Close the gap between reality and perception associated with several factors that typically discourage use of personal transportation devices (bikes, scooters, motorbikes). For example, these devices are quite safe relative to automobiles, but most people perceive otherwise. As another example, I wrote last month of the misperception of the consequences of adverse weather when traveling by personal transportation device.
2. Encourage/adopt plans and policies in the design of communities to support personal transportation. Bike lanes, charging stations, storage lockers/racks, bus racks, and other infrastructure improvements can reduce the transit time and increase the perceived safety of personal transportation.
3. Adopt taxation and user fee policies that closely tie costs to consumption. In the United States, we choose to pay for much of the cost of operating automobiles through broad-based taxes rather than through gasoline taxes and/or tolls. Such policies result in a detachment between consumer behavior and costs.
4. Establish peer and community groups that support and encourage the style/fashion/image of personal transportation.
I spent a week this month on Martha's Vineyard, a lovely island just off of the coast of Massachusetts. It is remarkable to observe how many vacationers use bicycles and motor scooters on this island. These are largely the same people who most of the year get around via the single-passenger automobile. What explains this behavior? Using a car requires an expensive ferry ticket and lots of planning. There are great bike paths--well designed and scenic along the main transit routes. The island is flat, making cycling a real pleasure. The weather is nice most of the vacation season. Dress is casual, and people can pretty much go anywhere in shorts and t-shirts, the same gear they can ride comfortably in. And, not insignificantly, there is a culture of acceptance of two-wheelers as part of island life. Given these factors, consumers respond rationally. Interestingly, with the possible exception of weather, these are all conditions that could exist in most of our communities in the United States.
My own sense is that communities are more livable and enjoyable when they encourage personal transportation. Those who agree should give some thought to how they can work in their own way to apply some of the levers that can influence individual choice.
HOW LIKELY AM I TO GET RAINED ON IF I COMMUTE BY BICYCLE, SCOOTER, OR MOTORBIKE?
First of all, if you live in California or the Southwestern United States, you probably don't spend much time worrying about rain. I'll assume that you live in a climate where the rainfall is 30 or more inches (750mm) per year. The question of how likely you are to get wet if outdoors at a given time of day turns out to be very tricky to answer precisely, and in fact, I won't be able to provide an exact answer.
Most rainfall data is collected on a daily basis. However, daily rainfall data is highly misleading as an indicator of what might happen, say, between 8:00 and 8:30 on a particular morning. For example, in Philadelphia, some rain might fall on 10 percent of days, but the chances of your getting wet for a 30-minute period in the morning are much less than 10 percent. This is because the average rain event is much shorter in duration than one day. (While there are exceptions to these generalizations, rainfall is remarkably consistent in its statistical properties across a wide variety of climates.)
Based on my informal observations of rainfall in the Eastern United States, I estimate that your chances of getting wet while riding in a 30-minute commute by bicycle, scooter, or motorbike are about 1 in 40 (2.5 percent). So, if you commute 200 days per year, you would get wet, on average, 5 mornings. (The mornings are of more concern than the afternoons, typically, as arriving home wet and dirty is less of a problem for most people than arriving this way at work.) Naturally, this estimate varies with climate, with your chances of getting wet in Denver much lower than in Atlanta.
Four points are worth emphasizing:
1. The odds of getting wet are much lower in reality than most people perceive them to be.
2. Getting wet is not that big a deal (although in the winter even I have to admit that rain can be pretty unpleasant). Keep a change of clothes at work. Carry a rain jacket if the weather is uncertain.
3. You can dramatically lower your odds of getting wet if you can adjust your departure time plus or minus even 30 minutes. These days you can observe on the internet (via Yahoo weather, for example) the regional radar for your area and can typically see rain coming a few hours in advance.
4. Taking a taxi to or from work even 10 times per year costs most people less than a couple of hundred dollars. This is what many of us would pay for only a month of parking or a month of auto insurance for a second car.
In sum, don't worry. Go ahead and ride. You probably won't get wet. Even if you do, it's not that big a deal. If you really don't like to get wet, watch the weather radar and either adapt your departure time or take a taxi when necessary.
P.S. The lawyers will want me to state the obvious: Rain impairs visibility. Braking distances increase when things are wet. Don't ride kick scooters in wet conditions. Be extra careful when riding bicycles and motorbikes in the rain.
HOW MUCH OF SOCIETY'S ENERGY CONSUMPTION IS FOR TRANSPORTATION?
This is nice opportunity to drag out a lot of statistics. These statistics are drawn from readily available public sources.
The world rate of energy use averages approximately 13000 gigawatts (13 trillion watts). The US rate of energy use averages approximately 3000 gigawatts (3 trillion watts). Thus, the US accounts for consumption of about 23% of the world's energy.
The distribution of energy consumption by source is as follows in the US. Globally, the distribution is only slightly different (a little less natural gas and hydroelectric, and a little more coal).
Natural gas 25.4%
Wood, solar, wind, geothermal 2.8%
Transportation energy is almost all derived from petroleum worldwide and accounts for an average of about 856 gigawatts (856 billion watts) of power. Thus, in the US, petroleum accounts for about 1239 gigawatts, of which 856 gigawatts or 69% is consumed by transportation uses. Therefore, to answer the question, transportation accounts for roughly 28% of all energy use in the US.
Energy in transportation is consumed by the following modes:
Commercial cars/trucks 43%
Passenger cars 37%
Commercial airplanes 8%
Rail Freight 2%
General Aviation 1%
Mass transit 1%
Note that although air travel is only 8% of the total US transportation consumption, it is disproportionately consumed by professionals and relatively affluent members of society. Consider this calculation. Your share of a round trip New York - California commercial flight accounts for the consumption of about 120 gallons of jet fuel. This is equivalent to the fuel for roughly two months of automobile use for most Americans. Commercial transport energy use is probably approximately correlated with general consumer economic activity. That is, when you spend money on goods and services, you probably consume energy in rough proportion to that spending.
HISTORICALLY, WHERE DID MOTORCYCLES COME FROM?
Motorcycles have evolved over about 100 years. As with most technological innovations, the motorcycle was developed simultaneously by several inventors in several geographic locations. The earliest successful enterprise was the Hendee Manufacturing Company of Springfield, Massachusetts (USA), which sold the Indian Motorcycle in 1902. You can see a photograph of a 1905 Indian motorcycle at this motorcycle museum site. (This model is very similar to the first model the company sold.)
Not surprising, the motorcycle evolved from the bicycle. At the turn of the century, the bicycle was one of the most important transportation devices in the world, and arguably was instrumental in the development of modern manufacturing. For a fascinating discussion of the history of early bicycle manufacturing, see David Hounshell's book From the American System to Mass Production, 1800-1932: Development of Manufacturing Technology in the United States (available via Amazon here). The motorcycle fairly quickly departed from the bicycle in style and design. As available power from the engine increased, pedals became superfluous. As attainable speeds increased, chassis requirements increased and motorcycles became larger and heavier. By 1932, the bicycle heritage is barely recognizable in the Indian product line and the more familiar modern motorcycle form has emerged. (Incidentally, by the 1930s, Indian and Harley-Davidson were the leading brands in the United States.)
In America, motorcycles evolved to satisfy an increasing desire for performance, speed, and power, largely as a recreational product. In much of the rest of the world, the motorcycle took a different turn, and evolved towards a practical transportation vehicle. In 1958, Honda introduced the Honda Supercub, which became the best selling vehicle in the world (over 30 million units sold, with variants still available today). It combined reliable, solid transportation performance with an affordable, practical design (photo). European and Japanese competitors continued to create practical and affordable motorcycles for the masses over the next couple of decades, with several Chinese and Indian companies following suit in recent years.
Interestingly, electric power in some ways brings us back full circle to the 1902 Indian. Because the power available from batteries and electric power is limited by cost and weight, electric motorbikes benefit from being super efficient. Successful electric designs must therefore borrow from the power conserving strategies of bicycle design. Electric-powered motorcycles are unlikely to be able to follow the hyper-power trajectory of American motorcycles of the last 50-60 years. Instead, I predict that we will see developments that more closely mirror those of the Honda Supercub and its descendants.
ARE THERE ANY NEGATIVE ENVIRONMENTAL IMPACTS ASSOCIATED WITH HUMAN-POWERED PERSONAL TRANSPORTATION (E.G., BICYCLES, SCOOTERS, WALKING)?
I am a long time proponent of human power for personal transportation, in part because human power offers the potential to reduce the use of fossil-fuel powered vehicles. This past week I read a very interesting article by David Coley, a scientist at the University of Exeter (UK), on the negative emissions associated with human activity (David A. Coley, "Emission factors for human activity," Energy Policy, Volume 30, p. 3-5, 2002). Dr. Coley's argument is simple: the energy for human-powered vehicles comes from food. Food production in the western world is quite energy intensive. Therefore, the net environmental impact of human power includes the impact of the energy required to produce the food that fuels the human.
Here is a summary of his analysis.
This is very interesting in that we would normally assume that walking and cycling have much, much lower emissions relative to driving a car. While I find this analysis fairly compelling, I want to add a few editorial comments and notes of caution in interpreting these findings.
HOW SHOULD PERSONAL TRANSPORTATION DEVICES BE REGULATED?
In this month's column, I veer with trepidation from the laws of physics to the murky world of politics and regulation. With the emergence of new categories of personal transportation devices, existing regulations have been stretched beyond their original intent. In my opinion, it is time for governments to be proactive in creating regulations that encourage clean, safe, efficient personal transportation. My positions are as follows:
In sum, we already know a lot about how to accommodate personal transportation devices in our society. Bicycles are an important analogy and have established sensible guidelines for low-speed lightweight vehicles. Sidewalks are for pedestrians. And, most larger, faster vehicles are clearly regulated (in the US and most other countries) by the motor-driven cycle and/or moped laws. Let's hope that as a society we can see our way through to establishing sensible regulations that encourage rather than inhibit electric-powered personal transportation devices.
WHAT IS WIND CHILL (AND WHAT DOES IT HAVE TO DO WITH PERSONAL TRANSPORT)?
Nova Cruz is located in New Hampshire, a location with honest winter weather. In cold-weather climates the weather forecast will often report the actual air temperature and then another "temperature" with the "wind chill factor." The wind chill factor is an attempt to account for the phenomenon that wind makes a person feel colder than they would otherwise feel in still air. Wind enhances what is known technically as "convective heat transfer," a fact known intuitively by anyone who has blown on a hot piece of pizza to cool it off. (Conversely, the flow of hot air over a cooler object enhances the rate at which heat is transferred TO that object, a phenomenon exploited by convection ovens to speed up cooking.)
The rate at which heat is transferred from a human body to the air on a cold day can actually be calculated (or measured). Given a person experiencing a particular wind speed and air temperature, the wind-chill "temperature" is that temperature in still air that would make the person feel equally cold. Wind chill is quite important to those of us who use open-air personal transportation devices (e.g., scooters, bicycles, motorbikes) in colder weather. Riding such a vehicle at a particular speed in still air is thermally equivalent (to a first approximation) to having wind blown at a stationary person at that same speed. Therefore, wind chill factors can be used to estimate how cold you will feel when riding a personal transportation device at a particular speed in air of a particular temperature. For example, let's assume that you ride at 15 miles per hour (25 km/hr) on a scooter or bicycle in still air. If the actual air temperature is 30 F (-1 C), the wind-chill "temperature" will be 19 F (-7 C).
I ride a scooter, bicycle, or motorbike pretty much every day all year round. Many people think I'm crazy. (By the way, I am somewhat crazy, but not because of this...) Let me offer two bits of advice to those of you who want to enjoy the pleasures of winter riding.
WHAT IS CNC MACHINING?
Nova Cruz makes many of the components of its products by "CNC machining." CNC machined parts are sometimes also called "billet" parts because the parts are made by sculpting a form from solid chunks or billets of material. For example, the aluminum deck on a Xootr Street, Venus, or Slimline is CNC machined from a solid slab of aluminum.
Machining refers to a manufacturing process by which material is removed by a cutting tool of some kind. Probably the most common machining process is "milling." A milling machine incorporates a spinning cutting tool which typically looks something like a big fat drill bit, but with a blunt end instead of a point. (If you are a woodworker, think of a big router bit.) A wide variety of shapes and sizes of cutting tools are available to create different shapes and sizes of geometric features. The milling machine has a clamping system to hold a chunk of material in place and the spinning cutting tool is then moved through the material in order to create slots, cavities, or shaped edges. Early milling machines were designed with hand cranks that allowed a skilled machinist to move the material relative to the cutting tool in order to create the geometry specified by an engineering drawing. The machinist used a combination of the dials on these cranks and measuring instruments such as calipers to create parts with the intended geometry. Typically, a milling machine has three orthogonal axes (x, y, and z) along which the material could be moved. Among the most venerable of milling machines is the "Bridgeport", still a mainstay of most prototype shops, including the one at the Nova Cruz R&D facility. A Bridgeport is about the size of a refrigerator and you can buy one for a few thousand dollars.
CNC is an acronym for "computer numerical control" which is a term that evolved as a result of historical developments following World War II. You are probably best off just forgetting about the underlying terms and just thinking of a CNC machine as a programmable, computer-controlled machine tool. The exact position and speed of the cutting tool on a CNC machine is specified by a computer program. In its most simple form, you could think of part of one of these programs as specifying that the cutting tool spin at 5000 revolutions per minute and move from point A to point B at a speed of 0.1 meters per second. Complex parts can be created by executing a program consisting of hundreds of simple instructions, each one of which involves directing the speed and position of the cutting tool. CNC machines like the ones we use at Nova Cruz also contain a carousel of different cutting tools, with the selection of a particular tool also controlled by the computer program. Very nice software tools allow engineers to create part designs and then automatically convert these designs into instructions that the CNC machine can interpret. So, for example, the curves that define the outside of one of the aluminum scooter decks are converted by the software into hundreds of points that form a path for the cutting tool on the CNC machine. The great thing about CNC machines is that an arbitrary geometric feature (subject to some basic constraints) can be quickly and easily created automatically. It is really no harder to machine a nice curved edge on a scooter deck than to machine a straight edge. (Imagine, in contrast, trying to create an arbitrary curved edge by cranking the handles for the X and Y axes on a Bridgeport...kind of like trying to draw a curve on an Etch-a-sketch.) We use CNC machines that are about as big as a mini-van or light truck, and they are pretty much fully enclosed (but have windows and lights so you can see inside). These machines typically cost more than $100,000.
Should you care, as a consumer, whether your product has CNC machined components? Yes and no. CNC machining is a nice way to make certain types of parts. We use CNC machining because it lets us create attractive parts very quickly and in low to medium quantities. However, these are mostly economic and technical benefits for the designer and manufacturer of the product. As a consumer, the only reason you should prefer a product with CNC machined parts is that they often look great because of surface finishes and geometric details. We like the CNC aesthetic a lot here at Nova Cruz. However, from a technical performance standpoint, you shouldn't care whether a part is made by CNC machining or by some other process. What matters is how the product performs.HOW MANY CALORIES ARE BURNED RIDING A KICK SCOOTER?
A calorie is a unit of energy. One calorie is the amount of energy (heat) required to raise the temperature of one cubic centimeter of water by one degree Celsius. Calories can also refer to the energy required to perform a certain amount of work. One calorie corresponds to the work required to lift a 1 kilogram mass a height of about half a meter (on planet earth).
Note that a "food" calorie is actually a kilocalorie, a thousand calories. That's right: a piece of bread containing 100 "food" calories actually contains 100,000 calories and therefore has enough energy in it to raise the temperature of 1000 cubic centimeters (1 liter) of water by 100 degrees Celsius. (Or to lift a 1 kilogram mass to a very large height.)
Your body is an amazing system, with the ability to convert food (fuel) into work (energy) through chemical and biological mechanisms. Like any system for converting fuel to work, your body is not 100 percent efficient. That is, it requires more than one calorie of food to provide enough fuel to your muscles to do one calorie of work. In fact, when engaged in vigorous activities, your body is around 20-33% efficient. Therefore, you must consume 3-5 calories of food for every 1 calorie of actual work you do. (This is good news if you are on a diet and bad news if you are competing in the Tour de France.) By the way, the rest of the energy value of the food is exhausted from your body as heat.
To propel an adult on a Xootr kick scooter at moderate speed requires about 100 watts of continuous power. At this intensity level, a rider would perform 86 kilocalories of work during 60 minutes of activity. (See notes for the arithmetic.) Assuming a fairly efficient kicking stride, the rider could probably operate at around 20 percent efficiency, so would burn 5 x 86 = 430 kilocalories of fuel for each hour of riding. Don't be depressed by how little this is (about half a Big Mac); studies indicate that exercise increases your metabolic rate generally resulting in greater caloric consumption throughout the day.
100 watts x 60 minutes x 60 sec/minute = 360,000 watt-seconds = 86 kilocalories
1 watt-second = 1 Joule 1 kilocalorie = 4182 JoulesHOW MUCH POWER DOES IT TAKE TO MOVE A PERSON AROUND ON A SCOOTER OR CYCLE?
I've seen scooters and cycles claiming 200 Watts and 18 mph top speed and others claiming 400 Watts and 12 mph top speed. How much power does it actually take to move a person around on a scooter or cycle?
Bicycles, scooters, and even automobiles are all governed by the same fundamental power requirements. At constant speed, the power required to move the vehicle and the passenger goes to three places:
1. The power required to overcome the rolling resistance of the wheels on the pavement.
2. The power required to overcome the wind resistance associated with moving the vehicle/passenger through the air.
3. The power required/provided to move the vehicle and passenger up/down any incline (if not traveling on flat pavement).
(NOTE: Stop here if you didn't like high-school physics.)
We can write this as an equation:
(Note that Total-power is the power delivered to the driving wheel of the vehicle net of any friction in the transmission and inefficiencies in the power system.)
To a first approximation, power-rolling-resistance is in turn determined by the weight of the vehicle/passenger (W), the speed of the vehicle (S), and a coefficient that characterizes the rolling resistance of the wheel (a). Power-rolling-resistance = aWS
To a first approximation, Power-wind-resistance is determined by the "frontal area" (F) of the vehicle/passenger (the area of the outline of the vehicle/passenger when viewed from the front), a coefficient (b) that characterizes the shape of the vehicle/passenger, and the CUBE of the speed (S x S x S).
Power-wind-resistance = bFS^3
Power-hill-climbing is determined by the grade of the hill (G), the weight of the vehicle/passenger (W), the speed (S) of the vehicle/passenger. Power-hill-climbing = GWS
So, the entire equation is:
Total-Power = aWS + bFS^3 + GWS = (a+G)WS + bFS^3
Before we do some calculations, we can make some interesting observations:
1. Total power required is strongly influenced by speed.
2. At high speeds, the effect of wind resistance will be very large (because it depends on S cubed).
3. Light vehicles/passengers have an overall advantage. In fact, although W does not appear in the expression for wind resistance, frontal area (F) is highly correlated with W, so overall size/weight pretty much influences all three categories of power consumption.
Now, some approximate numbers. (I use metric units, but provide some examples and conversion factors for those of you who think in English units.)
a = coefficient of rolling resistance
0.008 for high-pressure 700mm road bike tire
0.020 for a mountain bike tire
0.040 for a typical (e.g., 9 inch) pneumatic scooter tire
W is weight in Newtons (1 pound = 4.45 Newtons)
S is speed in Meters/Second (1 mph = 0.45 meters/second)
b = drag factor in kg/m^3 (This includes air density factor for sea-level air. Picky engineers: see note below.)
0.6 for a square-edged box
0.4 for most human-like shapes
0.2 for a egg-shaped object
F = frontal area in square meters
0.4 for a crouched racing cyclist and bicycle
0.6 for an upright cyclist and bicycle
0.8 for a standing scooter rider
G = height of climb/distance of climb (e.g., % grade)
Typical maximum railroad grade = 0.02
Typical maximum bike path grade = 0.05
Typical maximum overpass grade = 0.08
Maximum grade on Pike's Peak mountain road = 0.10
Powell St. in San Francisco (cable cars) = 0.17
1. How much power is consumed to propel a medium-sized (165 lb.) adult standing on a scooter with 9 inch pneumatic tires traveling at 12 mph?
W = 165 lb. = 734 Newtons
S = 12 mph = 5.4 Meters/second
a = 0.040
b = 0.4
F = 0.8 square meters
G = 0
Total-Power = (a+G)WS + bFS^3 = (0.04+0)734 x 5.4 + 0.4 x 0.8 x 5.4 x 5.4 x 5.4 = 159 + 49 = 208 watts
2. How much power is consumed in the same situation except traveling up a 2% grade at 12 mph?
now G = 0.02
Total-Power = (a+G)WS + bFS^3 = (0.04+0.02)734 x 5.4 + 0.4 x 0.8 x 5.4 x 5.4 x 5.4 = 238 + 49 = 287 watts
3. What happens if the scooter is going 20 mph on the flat?
now S = 20 mph = 9 meters/second
Total-Power = (a+G)WS + bFS^3 = (0.04+0)734 x 9 + 0.4 x 0.8 x 9 x 9 x 9 = 264 + 233 = 497 watts
Note that climbing a 2% grade (G=0.02) consumes the same power as rolling on tires with a rolling resistance of 2% (a=0.02).
Note that the power required to propel a vehicle does not depend on the power source. In other words, a scooter powered by kicking requires the same power for the same speed, weight, etc. as a scooter powered by an electric motor.
Finally, let me note that the vast majority of small electric vehicle manufacturers do not appear to know these basic laws of physics. I see a lot of scooters with advertised top speeds of 15-17 mph, yet with 9 inch pneumatic tires, and with motors and transmissions that can deliver only about 150 watts to the wheels. You can calculate for yourself that the specs must be highly exaggerated (or the manufacturers must assume that a small child is riding the scooter down a big hill...). Caveat emptor.
NOTE TO THE PICKY ENGINEERS (you know who you are): The expression for wind resistance is actually rho/2 * Cd * F * S^3, where rho is the density of air and Cd is a non-dimensional drag coefficient. Since rho is around 1.2 kg/m^3, the rho/2 term is around 0.6. To simplify these calculations, I included this factor of 0.6 in computing the "coefficient" b.DO ELECTRIC VEHICLES REALLY USE LESS ENERGY THAN GAS-POWERED AUTOMOBILES?
Consider two vehicles of essentially the same size, shape and weight; the first vehicle powered by batteries and an electric motor and the second by a gasoline-powered internal combustion engine. Assume that the electricity for the first vehicle comes from an oil-fired power plant. In this scenario, and for a given speed and distance, the electric vehicle would probably consume more fossil fuel than would the gas-powered car. This is because the power plant suffers from some inefficiency in converting oil to electricity and then this inefficiency is compounded by the losses in the electric vehicle in converting the electricity to motive power.
Here are some numbers:
An oil-fired power plant is about 35% efficient in converting the energy in the fuel to electricity.
An excellent electric vehicle can be 60% efficient in converting battery energy to useful work.
The net efficiency of converting oil to useful work is therefore 35% x 60% = 21%
A gas-powered automobile is about 25% efficient in converting gasoline to useful mechanical energy.
(There are some more details to these calculations, such as transmission losses in power distribution and transport/distribution losses for the fuel, but these numbers are approximately correct.)
So, on the face of it, the electric vehicle actually requires more fossil fuel to move a given speed and distance than does the gas-powered vehicle.
However, electric vehicles still make a lot of environmental sense. Here's why:
1. Typically, the places where vehicles are most densely used are exactly the places where pollutants are most harmful, whereas most power plants are located in less densely populated areas where pollutants are less damaging. This might be called the "displacement" argument.
2. Electricity can be generated by a lot of means other than burning of fossil fuels. Hydroelectric and wind power are both current methods in commercial use. In the future, solar, geothermal, and fuel cell technologies may be commercially viable.
3. Modern power plants are very well equipped with pollution-control technology. Although most cars have amazingly low emissions, about 2% of the cars on the road are badly out of tune and are serious polluters. (Of course, the C02 emissions are an inherent product of burning carbon-based fuels and cannot be "controlled" away...)
4. The vast majority of electric vehicles are highly optimized for energy efficiency. That is, they are smaller, lighter, more aerodynamic, and better at coasting than comparable gas-powered vehicles. So, many electric vehicles only require 1/3 or less of the power of a gas-powered vehicle of similar function.
Let me further offer three opinions about all of this:
1. The energy efficiency tricks played by electric vehicle designers could (and should) be played by designers of gas-powered vehicles. A 4 percent improvement in fuel economy of US passenger cars would eliminate any need to drill for oil in the Arctic. (Excuse my leap into politics...) Although I'm an environmentalist, I also believe in free markets. I just wish we Americans would agree to pay (at the pump) a reasonable estimate of the true long-run costs of our fossil fuel consumption. I think we'd see a 25-50% improvement in average fuel economy of our vehicles almost immediately. (Europe is Exhibit A in support of this theory.)
2. The best long-run design for automobiles is probably the so-called "hybrid." In a hybrid design, a small, efficient internal combustion engine provides a steady flow of power and then a bank of batteries and one or more electric motors are used to provide the peak power for acceleration and hill climbing. Such vehicles can be very efficient and have very impressive performance. The Toyota Prius and Honda Insight are just two examples of very sensible designs taking this approach.
3. The very best way to reduce fossil fuel consumption for transportation is to displace single-passenger automobile trips with trips using personal transportation devices such as scooters and cycles. Let's compare the fossil fuel consumption of a 5 mile trip in a Ford Explorer (a very popular sport utility vehicle) with a 5 mile trip on a Xootr eX3 electric scooter. The Ford Explorer would consume about 1/3 of a gallon of gasoline (1.3 Liters). The Xootr eX3 would consume about 75 watt-hours (or 0.075 kw-hr) of electricity, about 1 cent worth. This amount of electricity would require the consumption of about 1 tablespoon (20 grams) of oil back at the power plant. Now that's some serious conservation.WHAT IS AN AMP HOUR?
(I saw a battery rated at 12 amp-hours. I assume that an "amp-hour" is a unit of energy measurement, but I'm confused because I know my electric company measures energy in "watt-hours" or "kilowatt-hours". What gives?)
(WARNING!!! If you dont like geek speak, youll probably want to stop reading now and check back with us next month.)
An "amp-hour" is a measurement unit, often used to specify a quantity of electrical energy. (Technically, an amp-hour is actually unit of "charge.") One common use of amp-hours is to indicate the energy storage capacity of a battery. Put simply, an amp-hour is the amount of charge that a battery discharges in one hour if one amp of electrical current is drawn from it. Ostensibly, a 10 amp-hour battery can put out 10 amps for an hour or 1 amp for 10 hours. (Not quite true; see details, below.)
To understand amp-hours, we have to go back to basics, and actually digress slightly to discuss "watts" and "watt-hours". Recall that power consumption is typically measured in watts. For example, a bedroom night light might draw 5 watts, while a desk lamp might draw 100 watts. The total amount of energy consumed by a device is determined both by how much power it draws (its wattage) and by the length of time the power is drawn. So, for example, to estimate the amount of energy your desk lamp would use if left on for an entire day, you would multiply 24 hours by 100 watts, to get 2400 watt-hours or 2.4 kilowatt-hours (a kilowatt is 1000 watts). Your night light only uses 5 x 24 = 120 watt-hours (or 0.12 kilowatt-hours) in a day. Check out your electric bill next month, and you'll probably find that the kilowatt-hour, often denoted "kwh", is the way your electric company bills you for your energy use.
So, you might ask, if watt-hours are used to measure a quantity of energy, why aren't batteries rated in watt-hours instead of amp-hours? The answer is that they probably should be. However the historical convention is that a battery's energy capacity is given by specifying both a battery voltage (e.g., 12 volts) and it's "amp-hour" rating (e.g., 10 amp-hours). As I'm sure you recall, 1 watt is 1 amp of current at 1 volt, and watts = volts x amps, so you can calculate the watt-hours of energy in a battery by multiplying the battery voltage by its amp-hour rating. For example, a 12 volt battery with a 10 amp-hour rating would be able to discharge or store 12 volts x 10 amp-hours = 120 watt-hours of energy. However, a 24 volt battery with a 5 amp-hour rating would also be able to discharge or store 120 watt-hours of energy (24 x 5 = 120). So, all other things equal, a higher voltage battery requires a lower amp-hour rating to store equivalent energy.
One complication in all of this is that battery capacity is generally lower the faster you try to discharge the battery. You'd think that a 12 Volt, 10 amp-hour battery would be able to put out 120 watt-hours of energy. Unfortunately, for many types of batteries, the full 120 watt-hours of energy can only be extracted if the energy is drawn off very slowly, say 12 watts of power for 10 hours. If one tried to draw off 480 watts for 1/4 hour (still a theoretical total of 120 watt-hours), the battery would not deliver its full capacity, and much of the lost energy would go into heating up the battery. Specifically, lead-acid batteries are typically rated at the 20-hour discharge rate and have less than 60% of that capacity if discharged in one hour, while NiMH batteries can deliver nearly 100% of their rated capacity if discharged in one hour.
Let me conclude with two summary points. First, as a practical matter, if you want to do apples-to-apples comparisons of the total energy in two batteries, I recommend you convert to watt-hours by multiplying the amp-hour rating of the battery by the battery voltage. Only if the battery voltage is the same across two comparative batteries can you simply compare amp-hours to amp-hours. Second (and this is one of my pet peeves), as a consumer, you shouldn't have to care about amp-hours. You should only care about: how fast, how far, how heavy, how expensive... If an electric vehicle uses a high-capacity battery, that might mean that the vehicle has great range and speed. It might also mean that the vehicle is an inefficient hog of a machine and that a huge battery is required to get any kind of acceptable system performance at all. Conversely, if an electric vehicle uses a low-capacity battery, that might mean the scooter will have poor range and speed. It might also mean that the scooter was designed by a clever system designer, who knows how to use efficiently every watt of power.
Optional reading for the true die hard: Units of energy measurement are based on several different starting points. Many of you will remember that a calorie is the amount of energy required to raise the temperature of 1 cc of water by 1 degree Celsius. Calories are often used in the field of chemistry. (The "calories" used to measure the energy in food are actually "kilocalories". One "food" calorie is 1000 "chemistry" calories.) In most physics and engineering, the "Joule" is the most common unit of energy measurement. A Joule is the amount of energy required to lift 1 Newton of weight (about 1/5th of a pound) to a height of 1 meter. A Joule is also a watt-second, the amount of energy associated with the delivery of 1 watt of power for 1 second. Here are some common equivalences:
1000 calories = 1 kilocalorie = 1 "food calorie"
1000 watt-hours = 1 kilowatt-hour
1 watt-hour = 3600 watt-seconds = 3600 Joules
1 calorie = 4.18 Joules
Study problem: Work out how many Big Macs (about 1000 food calories) of energy are required for you to climb up a 100 story building (about 400 meters). How many 10 amp-hour 1.5 Volt batteries would be required to run a motor to lift your same weight up that height? Assume that both your body and the motor/battery system have an overall efficiency of 30%. That is, 30% of the energy you put in is converted to actual work.WHAT IS AIRCRAFT ALUMINUM?
Companies variously claim the use of "aircraft aluminum," "6061 aluminum," etc. in their products. What does all this mean? Aluminum is the most common metallic element on earth, comprising about 8% of the earth's crust. Pure aluminum is an element (Al), but is rarely used for structural purposes because it is relatively soft, weak, and hard to work with. Almost all aluminum used structurally in bicycles, scooters, automobiles, beverage cans, and other products is alloyed with small amounts of other elements such as copper, magnesium, manganese, and zinc.
When alloyed and processed in various ways, aluminum is amazing stuff. It can be as strong as some steels, but is about 1/3 the weight. It is highly corrosion resistant, easily formed and machined, and looks good to boot.
There are two numbering schemes commonly used for aluminum, one for "casting" alloys (alloys that are melted and poured or injected into molds to form parts) and one for "wrought" alloys (alloys formed into rod, plate, sheet and then cut, pulled, bent or otherwise processed mechanically to form parts). The two systems are pretty similar, so I'll focus on the designation of wrought alloys. Anyway, these are the alloys most commonly heralded by manufacturers.
Wrought alloys are categorized into the "thousands" series 1XXX, 2XXX, 3XXX,...,8XXX (9XXX is not used). You may have seen reference to specific alloys such as 2024, 6061, 7075. These are members of the 2000 series, 6000 series, and 7000 series, respectively. The first digit refers to the principal element alloyed with the aluminum. (Think of an alloy as a kind of mixture of one metallic element with another.) The alloying elements are as follows:
1xxx is essentially "pure" aluminum (>99% aluminum)
2xxx is alloyed with copper
3xxx is alloyed with manganese
4xxx is alloyed with silicon
5xxx is alloyed with magnesium
6xxx is alloyed with magnesium and silicon
7xxx is alloyed with zinc
8xxx is alloyed with other elements
The second digit in most specific alloys is 0 (denoting a "standard" version of a particular alloy), but any digit 0-9 is possible reflecting different versions of an alloy. (Think of this as a version number in software...). The last two digits (e.g., 61) refer to a specific recipe for an alloy in the series, reflecting a particular percentage of, say, magnesium, silicon, and aluminum. Each alloy has its relative advantages and disadvantages.
Some common alloys are:
2024 (used in many aircraft parts, very strong, not generally weldable)
3004 (easily stretched, used in aluminum cans)
6061 (tubing, extrusions, very machinable, weldable)
7075 (airframe parts, extremely strong, relatively expensive)
To make things more complicated, aluminum typically has a "temper designation" such as T6, which often follows the alloy designation (e.g., 6061 T6). The temper designation refers to the kind of heat treatment the alloy has been subjected to. Heat treatment is a pre-determined cycle of heating and cooling that results in a modification to the material properties. Many of these alloys have very different properties depending on how they have been heat treated. For example, 6061-T4 is about three times stronger than 6061 with no heat treatment, and 6061-T6 is about twice as strong as 6061-T4. In fact, the nature of the heat treatment of an alloy is typically a larger determinant of strength than the nature of the alloy itself.
So, when you see a manufacturer claim that their product is made with 6061 T6 aluminum all that means is that they use an aluminum alloy made of aluminum, magnesium, and silicon, and that this alloy has been heat treated according to the "T6" recipe.
Now, what about the designation of "aircraft" aluminum? This basically doesn't mean anything. Pretty much every alloy ever made has probably found its way into some part of some airplane, even if only on the lavatory door knob. While 2024 and 7075 are common aircraft alloys, many others are also used.
Finally, let me add an opinion to all of this: As fascinating as aluminum alloys are, the alloy designation of the aluminum in a product should be irrelevant to you as a consumer. In fact all you should have to care about is how well the product performs its intended function. For example, any decent engineer can make a strong vehicle frame using 7075 aluminum. A great engineer could make a frame that is just as strong using 6061. Heck, if an engineer can make a high-performance frame out of bamboo, more power to him/her. Frankly, I recommend you ignore and dismiss any specifications of alloys when reviewing product descriptions. Focus instead on things you do care about: how much does it weigh? how fast is it? how much weight will it carry? how far will it go?WHAT IS REGENERATIVE BRAKING?
As it accelerates, a battery-powered electric vehicle converts energy from its batteries to kinetic energy of the vehicle and rider. The idea behind regenerative braking (aka "regen") is clever. When using regenerative braking, some of this kinetic energy is converted back into energy stored in the batteries. In simple terms, regen uses the vehicle's electric motor like a generator, both slowing down the vehicle and reclaiming kinetic energy. I won't go into the details of how the motor is actually converted to a generator (at least not this month). Rather, I'll focus on two top-level problems that limit the effectiveness of regen.
1. You can't get all the energy back due to inefficiencies in the system.
Consider a given quantity of energy in a battery pack, say 1000 Joules (this is how much energy a 100 Watt light bulb uses in 10 seconds). Only about half of this energy, or 500 Joules, can be converted into the kinetic energy of the rider/vehicle due to inefficiencies in the batteries, electronics, motor, and transmission. The rest goes into heat. Now, consider what happens when the regenerative braking system is used to convert this 500 Joules of kinetic energy back to energy in the batteries. The system has a similar net efficiency (50%) going back the other direction, and so only 250 Joules make it back to the batteries. Using the values in this example, a rider accelerating up to speed and then applying the regenerative brake to slow down will have a net loss of 750 Joules and will recapture 250 Joules of the original energy in the batteries.
Note that 50% net efficiency is very high, and is achievable only by super-efficient vehicles like the Xootr eX3. A more typical efficiency for an electric scooter or bike would be 25-30%. For these vehicles, those 1000 Joules of energy starting out in the battery pack would end up as only about 60-90 Joules back in the batteries after regen. (This is one of the reasons most companies don't talk much about regen...)
In sum, you can't get all the energy back with regen, but 25% is better than nothing. (By the way, you CAN charge your batteries by applying the regen and propelling your vehicle under human power. However, we humans already have pretty weak motors and sapping a bunch of the power to charge the batteries will tire you out pretty quickly. You're better off just kicking or pedaling to the nearest charger.)
2. The maximum deceleration that regen can provide is limited by the maximum current that can be handled by the electrical system of the vehicle.
Here is a startling fact. A small electric vehicle like an electric scooter or a electric bicycle is typically powered by a motor that can produce 200 Watts to 750 Watts of power to accelerate the vehicle. However, braking that most people consider "strong" for such vehicles requires that up to 5000 watts of power be absorbed by the brakes! Unfortunately, with regenerative braking, the braking power must be handled by the motor, controller, and batteries of the vehicle. For a 24 volt system, 5000 watts is equivalent to over 200 Amps of current...about what is used in a big welding machine. (In fact, "welding" is not a bad image for what would happen to the motor, batteries, and electronics of a small vehicle trying to provide this much regenerative braking.)
As a result of the very large power absorption requirements for braking, regen is typically used as a supplemental brake for slowing the vehicle, but is of limited value for panic stops or extremely high speed braking. To provide more than modest braking forces, regen would require huge motors, batteries, and controllers, which would be prohibitively large and costly.
For those of you trying to brush up on your high-school physics (or for those of you TAKING high-school physics) here's the math:
We know that
Force = Mass x Acceleration (where in the case of braking, acceleration is
negative, or "deceleration")
Power = Force x Velocity
If we assume that
mass=100 kg (equivalent to ~220 lbs, for the rider and vehicle)
acceleration= 5 m/s^2 (~0.5 g, half a "g" feels like a nice automotive brake)
velocity= 10 meters/sec (~22 mph)
Force= 100x5= 500 N (~100
Power=500x10=5000 watts (!!!)
(As a fun exercise for the reader, run those numbers for the power dissipated when doing a panic stop at highway speeds in a sport utility vehicle.)WHAT ARE BRUSHLESS MOTORS?
Brushless motors are super efficient, small, low friction motors. They are one of the technologies that allow Nova Cruz to make the fastest and most powerful portable electric scooter in the world.
(WARNING: Geek speak ahead! If these things frighten you, stop reading now and check us out next month. If not, please read on.)
First, I want to share a very useful web link with my readers. Check out "How Stuff Works" at http://www.howstuffworks.com/motor.htm . How Stuff Works is a great site generally, but it also has a very nice explanation of a plain old permanent magnet motor.
In sum, a plain old permanent magnet motor (like those found in inferior electric scooters) consists of a ROTOR (the spinning part) with a coil of wire wound around it and a STATOR (the stationary part on the outside) with several permanent magnets stuck to it. The rotor wants to move when electrical current is passed through its coil. This is because the current generates a magnetic field (the coil is an electromagnet) which is repelled by the magnetic field from the permanent magnets on the stator. If you think about it, there's a basic problem with this scheme. You have to have a way to get the electrical current from the power supply to the coils on a spinning rotor, and you have to energize the coil at just the right point in the rotation of the rotor so that it is repelled in the right direction relative to the magnets on the stator. These problems are solved in plain old motors with BRUSHES. Most plain old motors have two brushes. (Look on some plain old motors, like on your cordless drill and you'll see two little caps screwed into the opposite sides of the housing. These are probably the access ports to replace your motor brushes.) Each brush is generally a block of carbon (looks like a big hunk of pencil lead) held with a spring against a contact surface on the rotor. A power supply (e.g., battery) wire is connected to the brush and the brush makes contact with the rotor in a way that the coil on the rotor is connected to the brushes at just the right time in the rotational cycle of the rotor. This is a tidy idea, and it's actually pretty amazing that people figured out how to make this work and how to get the brushes to last a long time. However, there are a couple of big problems with these motors. First, there is a lot of electrical resistance where the brush contacts the rotor. As a result, when the motor is working very hard, a lot of the electrical power is lost when it is conducted across those contacts. Second, the coil on the rotor can get very hot (due to the electrical resistance in the wire that makes up the coil). However, this coil is crowded into the center of a motor surrounded mostly by air and the heat has a hard time escaping. This means that a motor of a given size can only carry so much electrical power before it overheats.
Brushless motors solve both of these problems (as well as lots of others...). The first thing you notice about a brushless motor is that it has several coils of wire wound into the stator (the outside stationary part of the motor). This means that the coils can be in great contact with the motor housing, which can conduct away the heat generated as electricity passes through the coils. In the case of the Xootr eX3, we bond our motor stator into a six pound chunk of aluminum (our deck), so that we can get lots of heat out of the motor and the motor can be very small for the amount of power it puts out. The second thing you notice about a brushless motor is that the rotor is very simple. It's just a bar of steel with permanent magnets stuck to the sides. When a coil on the stator is energized, it repels a magnet on the rotor and the rotor moves. Simple, eh? The problem is how to energize the right coil at just the right time, so that the rotor is always being repelled and continuously generates mechanical power. In a brushless motor, this switching on and off of coils (called "commutation") is done with a little computer (yes, electronics are required...). Ironically, brushless motors are actually much simpler mechanically than plain old motors. However, the catch is that you need a little computer to watch the rotation of the motor and switch on and off the right coil on the stator at the right time to keep the rotor moving.
So, coils on the outside allow the motor to get rid of more heat which allows a smaller brushless motor to do the work of a larger plain old motor. And, because there are no sliding electrical contacts between brushes and rotors, the electrical efficiency of brushless motors is very high. A third benefit is that a brushless motor has essentially no friction (remember...no rubbing brushes). For the eX3, this means that the scooter is fully kickable, with essentially no mechanical drag. Finally, let me note that there are lots of other advantages to brushless motors, including the ability to set the "timing" of the switching of the coils for better efficiency (like the timing of the spark on an automobile engine) and the ability to easily regulate the electrical power applied to the motor. In sum, they are definitely the way to go...except for one problem. Brushless motors are currently several times more expensive than plain old motors. This is why a Xootr electric scooter will cost you more than an ordinary electric scooter with a plain old motor. You get what you pay for. If you want small, light, fast, and efficient, brushless is the way to go.
Copyright 2002-2008, Karl Ulrich, all rights reserved. "Dr. Beetzwaken" is a trademark of Xootr LLC.