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Old Dec 23rd 2013, 07:30 AM   #1
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Car vs. airplane power

Hi all,
I have been trying to get my head around the relation between power, acceleration and thrust (force). In a car, the acceleration decreases when doing 0-60 mph as the transmission shifts up, although the same power (kW) is applied to the wheels. That seems natural since the torque on the driving wheels goes down with each gear shift. This should mean that under constant power (kW), acceleration starts at its highest and inevitably drops with increasing speed (notwithstanding drag).
In a jet aircraft however, force – which is proportional to acceleration - appears to be constant from start to take-off. How is this possible? Does the jet engine gradually gain power from the increasing intake air pressure throughout the acceleration? If the available power were constant, logically force/thrust/acceleration would drop.
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Old Dec 23rd 2013, 12:06 PM   #2
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Originally Posted by nevermissedabeat View Post
In a car, the acceleration decreases when doing 0-60 mph as the transmission shifts up, although the same power (kW) is applied to the wheels. That seems natural since the torque on the driving wheels goes down with each gear shift. This should mean that under constant power (kW), acceleration starts at its highest and inevitably drops with increasing speed (notwithstanding drag).
Your description is not quite accurate. If you assume that power is constant regardless of RPM, then indeed torque decreases with increasing engine speed, since power equals torque times RPM. But torque does not "go down" with each shift - the very reason you shift is to keep the engine working where it's most efficient. Actually for most car engines torque increases with increasing RPM to around 4000 RPM or so, then starts to trail off. Since power is proportional to torque times RPM, horsepower typically maxes at a higher RPM before trailing off.

Originally Posted by nevermissedabeat View Post
In a jet aircraft however, force – which is proportional to acceleration - appears to be constant from start to take-off. How is this possible? Does the jet engine gradually gain power from the increasing intake air pressure throughout the acceleration? If the available power were constant, logically force/thrust/acceleration would drop.
For a jet engine we typically model it as constant thrust, regardless of speed. This is because the mechanism of a jet engine involves accelerating burned fuel mass out the back, and that acceleration is constant regardless of the plane's speed. Hence power, which again is force times velocity, increases with the plane's velocity.

One thing to remember in all this is that while people often talk about an engine's power, the truly important performance metric is torque for car engines and thrust for a jet engine.
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Old Dec 23rd 2013, 04:25 PM   #3
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Power, torque etc.

Thanks for comments, ChipB
I do not agree to your statement that torque is what counts in a car engine. Torque is essentially a static entity. What makes the car accelerate is power, i.e. the amount of dynamic energy you can add per time unit. Whether that is done with a 4000 RPM long-stroke diesel at torque M or an 8000 RPM short stroke gas engine at M/2 makes no difference. Maximum engine torque is wrongly used to describe cars’ performance, especially by ignorant motor journalists. That has more to do with available power in normal driving, but then “power at half of top RPM” would be a better measure, I think.
Coming back to the subject; the force felt when pressed against the car seatback during acceleration is highest right after start. That force is directly proportional to the total torque of the driving wheels (i.e. where it counts). This torque goes down with each shift, because of the increasing gear ratio. Approximately the same amount of power is applied throughout the acceleration (assuming smooth shifts, throttle and RPM nearly constant), so wheel torque must decrease proportionally to the increasing wheel rotation. Acceleration is proportional to force (a=F/m), therefore also it must decrease. Am I right?
The heart of the matter is this: why does a car not accelerate at a constant rate when a constant power is applied? Maybe that is natural, in which case there must be a relevant formula.
I am still puzzled with the fact that a jet appears to give a constant push against the seatback as acceleration continues. Unless I am totally mistaken, jet power must increase in that process.
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Old Dec 23rd 2013, 06:52 PM   #4
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Originally Posted by nevermissedabeat View Post
why does a car not accelerate at a constant rate when a constant power is applied? Maybe that is natural, in which case there must be a relevant formula.
As you note power is the rate of energy per second being expended, to overcome drag and to accelerate the car - that is to increase the car's kinetic energy. The reason acceleration isn't constant is because kinetic energy is propotional to velocity squared. To go from 0 MPH to 10 MPH requires 10^2-0^2 = 100 units of energy, but to go from 10 to 20 MPH requires 20^2-10^2= 300 units of energy. Thus under constant power it takes 3 times longer to go from 10 to 20 as from 0 to 10. Actually it takes even longer than that because of the added drag due to higher wind resistance.

Originally Posted by nevermissedabeat View Post
I am still puzzled with the fact that a jet appears to give a constant push against the seatback as acceleration continues. Unless I am totally mistaken, jet power must increase in that process.
Not really. Jet engines are measured in thrust, not power, because of the confusion that arises in considering how speed is measured. In the case of a jet engine power would be measured as the thrust of the exhaust gas times the velocity of the exhaust gas relative to the engine, and that stays fairly constant regardless of the plane's velocity.
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Old Dec 24th 2013, 02:45 AM   #5
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Got it!

Thanks again, you explained the relation energy/speed well.
In the comparison car vs. jet aircraft, I must have missed the fact that different references for speed and force are used.

Another question: Is it true that in a jet aircraft – unlike a propeller plane - – engine power can remain fairly constant at high altitude, in spite of the dilution of oxygen? The reason would be that as speed increases - thanks to lower drag – air entering the combustion chamber is compressed.
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Old Dec 26th 2013, 01:42 PM   #6
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There are many influences on the optimum altitude for an aircraft.
The entire aircraft is designed to be optimally efficient in a quite narrow range of speed and altitude.
The wings and engines in particular are precisely tuned to work best at the aircraft's cruising conditions.
Thus the simple relationship you indicate is not really that simple.

Also note that the major source of thrust in a (commercial) jet is actually from the "bypass" air from the main fan at the front of the engine, not from the jet itself.
The fan is in many ways just a glorified propeller.
Military jets have a much lower bypass ratio, allowing supersonic performance but grossly reduced efficiency.
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