Wednesday, March 12, 2008

The New 'Bent

Three years ago in a state of complete mania, I designed my first electric car. It was what I called a 'travel car,' in that it was designed to be used in conjunction with other modes of transportation, such as train, bus, plane, etc. It was also designed for business travelers making overseas journeys who did want to have to rent a car when they got to the airport. The chassis was collapsible and the entire car fit into two suitcases that could be checked on an airplane (The geometric configuration was completed on the back of a napkin while waiting for chinese food at Lucky's on Baltimore). There were four independent hub motors and it ran off lithium batteries which were wired in series-parallel to comprise the floor. The shell was removable and rollable and composed of thin-film flexible PV polymer for complimentary solar recharge (after a good bit of research, I have concluded that solar power is better suited for applications other than EVs). It weighed less than 100 lbs.

This project never got off the ground, mostly in part because I was too sick to think straight at the time. The concept of a collapsible LEV, though, was a good one, I thought, though it was not without its shortcomings. One was its classification as a 'car': this brought with it the possible harassment by law enforcement, the dangers or traveling at highway speeds and having to compete with other cars for road space, licensing, the necessity of stricter adherence to traffic laws, compromised portability, etc.

Then it occurred to me that its bikes, not cars, that I have grown up working on. Why not stick with what I know? Bikes have so many advantages over cars, but cars also have advantages over bikes as well. Is there a way to produce a sick hybrid that is capable of incorporating the advantages of both?

When the weather breaks I am hoping to take a weekend to visit my friend Andy in Ithaca. I don't want to drive or take the bus the whole way. It's too far to ride on pedal or battery power alone. I made a trip to Reading last year with my 33cc Robin engine hooked up to an old Schwinn cruiser and averaged about 25 miles per hour; (top speed was around 33mph). Using a gas-powered engine of size 49cc or less on a bicycle is within PA DOT law, but the wind resistance on a conventional upright setup was preventing me from doing much more than 30mph for a sustained period of time. If I wanted to go faster, I would have to either get a bigger engine...or get 'bent.

Recumbent bicycles ("'bents") employ a laid back riding style and typically use smaller wheels. This results in a more aerodynamic shape due to the reduced frontal area they achieve by traveling closer to the ground. World records have been set on fully-faired recumbent, with riders covering over fifty miles in a one-hour period.

Walter Zorn's Bicycle Speed and Power Calculator has been invaluable in the number-crunching part of this R&D process...because it keeps me from having to actually crunch numbers. To give you an idea of all the factors that go into determining speed vs. power demands based on variables such as weight, frontal area, slope, rolling resistance, etc., here is the old school pen and paper way to go about such calculations:

P Rider's power
V Velocity of the bicycle
W Wind speed
T Air temperature (reduced to deg. Kelvin) (influences air density)
HNN Height above sea level (influences air density)
rho Air density
rho_0 Air density on sea level at 0° Celsius (32°F)
P_0 Air pressure on sea level at 0° Celsius (32°F)
m Mass of the bicycle (influences rolling friction, slope-dependent pull-down force, and normal force)
M Mass of the rider (influences rolling friction, pull-down force, and the rider's frontal area via body volume)
A Total frontal area (bicycle + rider)
Cw Air resistance coefficient
g Gravitational acceleration
Cr Rolling resistance coefficient
Cm Coefficient for transmission losses and losses caused by tire slippage (the latter can be heard during powerful pedal strokes at low speeds, for instance by their echo when you're riding along a vertical wall)
stg Inclination (grade) of road (unit: percent)

rho = rho_0 * (273/T) * e-rho_0*g*HNN/P_0 (air density via barometric formula)
Equation for rolling friction force and pull-down force (pull-down force plus normalized rolling friction force on inclined plane)

Equation for the required human power

if a2 + b3 > 0
if a2 + b3 <>
with: Expression "a" of the velocity equation and Expression "b" of the velocity equation

Needless to say, I prefer to let the computer do the work for me.

The Robin engine has a max output at 7,000 rpms of 1.8kw. When this is computed given certain constants (hands on top, slope=0, racing tires, etc.), top speed is calculated to be 40.6mph. Of course you cannot run a 33cc engine at 7,000rpms continuously or it will blow up. That would mean cruising speed would be closer to 30mph.

Like I said, for a 200+ mile bike trip I would like to average somewhere in the 40mph range. I don't think I would like to gear the bike for a top speed higher than 50mph, but I would like to be able to achieve that speed for bursts when needed. Since the maximum output of the motor tops out at 40.6mph in a conventional setup, I wondered how the power requirements would change with a 'bent setup. According to Zorn's calculations, a 'bent lowracer would be able to achieve a top speed of 57.4mph at 7,000 rpms and maintain a continuous output of 1.1kw indefinitely averaging 48mph. Not bad, not bad at all.

I was fooling around in the basement last night after getting off the phone with Andy and pieced together a prototype 'bent from scrap in the basement. The parts used include: 20" rear wheel with 3 speed internal hub; 12" front wheel with coaster brake; front fork with underseat caliper brake; chopped downtube and 3/4 of headtube of adult road bike; 12" fork. The parts came from 1 adult and 1 child's bike and the total setup minus the 10 lb engine weighs in at less than 15 lbs. I still need to add a bent-form backrest, gearing, and front-wheel drive cranks, but everything is more or less there. The bike employs a 6 (3/3) speed internal transmission using two Sturmey Archer 3 speed internal hubs for jackrabbit starts and high-end topspeed. The best part? The bike can be collapsed at one joint (where the fork tube slides into the downtube) in less than 5 seconds and stored in a 20x28x10 suitcase for travel. It is a very simple design with few moving parts (the less parts, the less prone to failure). The gas engine averages 250 miles per gallon. Ithaca is 224 miles from my home, which means it would cost me around $3 to travel the distance averaging 48mph, arriving in less than 5 hours. Like I said, not bad at all.

I hope to have this tested and out on the road in the next few months. It seems like a promising alternative to both full sized autos and bicycles for longer trips in which bicycling is not a practical option. Hopefully my sleepless nights will offer the world an example of a low-cost, energy efficient alternative to the private automobile and incite revolution by summer's end.

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