|MadSci Network: Engineering|
Hi, Many people are often confused about power and energy. Let's start from the beginning, with some basic equations: Energy = Force * distance For a mass m moving at a speed v, the energy E is: E = 0.5 * m * v * v Energy can be measured in Joules (J) or British Thermal units (BTU). 1 BTU is equal to roughly 1055 Joules. If a 2100 pound car is travelling at 60 miles/hour, the energy is about 342600 Joules or 325 BTUs. This is the same amount of energy required to accelerate the car from 0 to 60 miles/hour on level pavement. This is independent of acceleration, it doesn't matter if it takes 6 seconds or 60 seconds, it's the same amount of energy. Energy is always conserved, meaning it can't created or destroyed, it can only change form. Power = rate of energy Power can be measured in Watts (W) or Horsepower (HP). 1 HP is the same as 746 Watts. Power, unlike energy, is not always conserved. If we have a system where energy is flowing at a constant rate, then power is conserved, meaning the power in is equal to the power out. For standard cars, power from the engine is delivered to the wheels through a transmission. There are some losses due to the transmission, air conditioner, alternator, and other systems, but this is not considered a significant loss. If the air conditioner is turned off, your headlights are off, and you have a manual transmission, the losses will be not more than a few percent. Automatic transmissions only increase losses. The gear ratio is a transmission does not change power output. Remember, power is conserved in this case. There might be some slight change in power loss for different gear ratios, but for the most part, it's insignificant. Since we know power is the rate of energy, we can divide the energy calculated above by the time required to produce the energy. If it takes your car 6 seconds to go from 0 to 60 miles/hour, then the power is about 57000 Watts or 76.6 HP. Keep in mind, this is the average power, it doesn't tell us the power at any time during the acceleration. We would need detailed speed measurements from start to finish to calculate that. Given these numbers, I would guess the engine is capable of producing 150 HP or more. How did I come up with that number? Internal combustion engines, like gasoline, Diesel, and even turbines, do not have a flat power curve. The power output is zero at zero RPM and increases more or less linearly until some peak. In stock gasoline engines, the peak power is at 5000-6000 RPM or so. As a rule of thumb, the peak is generally 1000 RPM below red line. So if you could run your engine at 1000 RPM below red line, then you could achieve near peak performance. If watch your tachometer, I would guess that the RPM averages much less than that, maybe even half. That's why you are getting only half of the power the engine is capable of producing. RPM, power and torque are all related. Torque is simply power divided by RPM. The power out of a transmission is the same as the power in (minus small losses), but the RPM is different depending on the gear ratio. If the output shaft spins at half the speed of the input, then the output torque is double that of the input. RPM doesn't really matter in the end as far as power is concerned, remember, power is conserved. Changing gear ratios does not change the power, it only affects torque and RPM. It's easier to start with calculate power and work out RPM and torque if you need it. You can do it the other way, but it's easy to make mistakes. The reason most cars have a transmission at all is because gasoline engines cannot produce torque over a wide range of RPM, particularly at zero RPM. Diesel electric locomotives and subways do not have transmissions with variable gear ratios because they use electric traction motors instead of transmissions. Electric motors can produce torque over a wide range, even at zero RPM. This is known as the stall torque. Note that steam locomotives don't have transmissions either. That's because piston driven steam engines can also produce very high stall torque. In summary, here is all you need to know: Energy = 0.5 * mass * v * v Power = Energy / time (if power is continuous) Power = RPM * Torque That's it. To use these equations with your car, all you need to know is the mass, speed, and time. Be careful to use consistent units in your calculations. I tend to start with MKS units and then convert to other units if needed. That's why I use Watts instead of HP and kilograms instead of pounds. Good luck!
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