For back-of-the-envelope gear figuring, I've found this formula helpful: P = IV = Fs = mas
Power = current * voltage = force * speed = mass * acceleration * speed Assume a 400 Amp, 100 volt, 2000 kg S10 truck. Give it one gear for 80 mph top speed, and assume the knee to constant power (like Lee's graphs below) occurs at 40 mph (~ 20 m/s) (where you drop out of current limit). a = IV / (ms) = 400A * 100V / (2000kg * 20m/s) = 1 m/s^2 = 0.1 g Since g = 10 m/s^2, this is only 1/10 of a g, or enough to go up a asin(0.1) = 6 degree slope. 0 to 60 mph would take about 30 seconds for no wind or rolling resistance, and longer in the real world. Definitely a good candidate for multiple gears! Now what about the EV1? a = 137 kW / (1500 kg * 20 m/s) = 5 m/s^2 = 0.5 g This is 1/2 g, good to climb about a 30 degree hill, and good for 0 to 60 mph (no tire or wind resistance) of about 5.5 seconds. Looks pretty good with one gear! But note it took triple the power to do that (roughly three times the voltage). Another reason to have gears would be if you need to climb steep hills. Many motors have trouble keeping cool for high power, low rpm operation. I've done the math a few times, and keep coming back to using a transmission. It would be tough to make a conversion light enough and powerful enough that it'll be faster with just 1 gear than several, even taking into account times to shift. I figure, too, if 1 gear is that great I can just stick it in 2nd or 3rd and remove the shift lever later. Finally, the tranny makes for a very convenient spot to hang the motor! Otherwise I'm doing a bunch of custom gears or belts or something. --- Lee Hart <[EMAIL PROTECTED]> wrote: > Sigh... we aren't thinking very clearly about the one-speed vs. > multi-speed situation. It doesn't matter if it is an AC vs. DC > drive. > What matters is that the motor+controller+transmission system > produce > *enough* torque over a wide enough speed range. > > The torque-speed curve for *BOTH* an AC drive and a DC drive looks > like > this: > > torque > |__________ > | \ > | \ > | \ > | \ > |______________\____speed > > The flat portion is when the controller is in current limit; fixed > current = fixed torque. The falling portion is when the controller > comes > out of current limit, and battery voltage is limiting torque. > > If the peak torque is high enough to spin the wheels, and the top > speed > is high enough to reach your maximum desired road speed, then the > motor+controller is "big" enough to work without a transmission. A > single gear ratio can satisfy both your max torque and max speed > needs. > > If you pick a smaller motor+controller, its max torque and/or max > speed > capability is less. But, you can boost the torque at low speeds > with a > transmission. > > torque > |____low gear > | \ > |_____\______high gear > | \ \ > | \ \ > |________\_____\____speed > > Obviously, the peak horsepower isn't as high; but you have the same > torque (hill-climbing and accelleration capability) at low speeds, > and > the same top speed as the more expensive motor+controller without a > transmission. > > Or, you can look at it from a horsepower point of view. Horsepower > is > torque times speed, so the horsepower curve for the large > single-speed > motor+controller looks like this: > > horsepower > | _ > | / \ > | / \ > | / \ > | / \ > |/_____________\____speed > > And a 2-speed transmission and smaller motor+controller horsepower > curve > looks like this: > > horsepower > | > | low gear > | _ _high gear > | / \ / \ > | / \/ \ > |/___/_\_______\____speed > > The smaller motor+controller+transmission delivers less peak > horsepower, > but delivers its smaller horsepower over a wider range. In fact, an > ideal infinitely variable transmission would deliver constant > horsepower > over a wide range, so a smaller motor+controller+transmission would > outperform a larger single-speed motor+controller. > > The devil is in the details. Exactly how lossy is your > transmission? How > fast can you shift? How wide a speed range can you get per gear > ratio? > -- > Lee A. Hart Ring the bells that still can ring > 814 8th Ave. N. Forget your perfect offering > Sartell, MN 56377 USA There is a crack in everything > leeahart_at_earthlink.net That's how the light gets in - Leonard > Cohen > __________________________________________________ Yahoo! - We Remember 9-11: A tribute to the more than 3,000 lives lost http://dir.remember.yahoo.com/tribute
