HP vs Torque vs Fuel Efficiency

[cRiPpLe_rOoStEr]

The power vs. torque debate is far away from an end...

[sendler]

Here is an interesting quote by DieselMaxPower at the Honda site which explains the conundrum of the power at the rear wheel not being multiplied by using a lower gear even though the vehicle does accelerate much faster. An example would be The CBR250R with an engine power peak at 8,700. If you are rolling along at a steady speed in first at 8,700 rpm, and then crack full throttle, the bike will accelerate violently. We can feel this very obviously. Now do the same in top gear. The bike is felt to start going faster but the rate of acceleration is much, much less. Even though we used the same amount of power from the engine and at the wheel. The acceleration is much greater with the lower gearing but we have put the same amount of power to the ground over time as in the higher gear. There must be some quantity that is increasing at the same rate in either gear (disregarding the higher resistance of speed to wind drag in top gear).
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Ready?
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The ENERGY of the system is increasing at the same rate in either gear. But we are very bad at perceiving energy so it seems like top gear does very little and first gear is doing much more with the same amount of power.
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Example of how bad we are at perceiving differences in energy:
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Cruising along at a steady speed in a car so you can't feel the wind, 10 mph feels pretty much the same as 70 mph. But 70 mph has much more energy and would be a very bad time to run into a wall.
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From DiesleMaxPower
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Honda CBR250R Forum : Honda CBR 250 Forums - View Single Post - Gearing: Horsepower's Better Half
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"Torque doesn't do one thing while horsepower does another. Torque is a measure of what's happening to the bike. So is horsepower. It depends on what you want to look at. Torque can give you a way to look at the accelerations. This is great for most humans because we can perceive things like position, speed, and acceleration. Horsepower lets you look at energy. Humans don't have a good way to perceive energy, except for maybe temperature changes which we don't include. When we analyze the dynamics of the bike we look at the speed of the bike (thats the momentum side) and the kinetic energy (thats the energy side). In the simple analysis we're doing now the two are so simplistic that they will always be consistent with one another. It doesn't matter if you decide that torque moves the bike or horsepower. The reason I like to look at HP because the math is much easier, as we've shown with our torque charts. You don't need to transform it through gears."

[darcane]

Originally Posted by sendler

Here is an interesting quote by DieselMaxPower at the Honda site which explains the conundrum of the power at the rear wheel not being multiplied by using a lower gear even though the vehicle does accelerate much faster. An example would be The CBR250R with an engine power peak at 8,700. If you are rolling along at a steady speed in first at 8,700 rpm, and then crack full throttle, the bike will accelerate violently. We can feel this very obviously. Now do the same in top gear. The bike is felt to start going faster but the rate of acceleration is much, much less. Even though we used the same amount of power from the engine and at the wheel. The acceleration is much greater with the lower gearing but we have put the same amount of power to the ground over time as in the higher gear. There must be some quantity that is increasing at the same rate in either gear (disregarding the higher resistance of speed to wind drag in top gear).

Here's the problem... you can't disregard air resistance at higher speeds. That's like saying granite would float in water if you disregard gravity.

In top gear, you use a significant amount of your power due to wind resistance and friction. Only the remainder is used to accelerate the vehicle. Since you have less available power to accelerate the vehicle, you will accelerate slower.

It is also more "violent" in low gears because you have more torque at the wheels which is more likely to get the tire to lose traction or for the reaction to lift the nose of your vehicle upwards.

[sendler]

Originally Posted by darcane

Here's the problem... you can't disregard air resistance at higher speeds.

So the difference between 1st and 6th in the acceleration you feel is entirely due to wind resistance?

[darcane]

Originally Posted by sendler

So the difference between 1st and 6th in the acceleration you feel is entirely due to wind resistance?

Yes, I believe so. Well, that and resistance due to friction (It increases with speed, but not exponentially).

Assuming, of course, all else remains the same (engine speed/power, weight, etc) and you only change gear ratios.

[sendler]

Originally Posted by darcane

Here's the problem... you can't disregard air resistance at higher speeds. That's like saying granite would float in water if you disregard gravity.

In top gear, you use a significant amount of your power due to wind resistance and friction. Only the remainder is used to accelerate the vehicle. Since you have less available power to accelerate the vehicle, you will accelerate slower.

It is also more "violent" in low gears because you have more torque at the wheels which is more likely to get the tire to lose traction or for the reaction to lift the nose of your vehicle upwards.

But consider this: What about the turbo diesel trucks in the link which all have a basically FLAT power curve. Could you then choose from 3rd, 4th, or 5th which would give the same exact power and road speed? Just a different rpm and torque multiplication. And expect the exact same level of acceleration? Crazy topic huh. I think 3rd will accelerate much harder.
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[mort]

Originally Posted by sendler

So the difference between 1st and 6th in the acceleration you feel is entirely due to wind resistance?

Hi sendler,
No, it is the road speed that matters the most. Power makes the thing go and the amount of power required at any speed depends on the speed.
If you use the ecomodder calculator here (note: the aero and rolling resistance forces are shown in Newtons) and think motorcycle... you get 30 hp needed to keep going 100 mph.

But the amount of power it takes to accelerate also depends on your speed. The acceleration is just like any other force being applied to the bike. Let's say you want to accelerate at 1 g, and you are going 50 mph. Again according to the ecomodder calculator, that would require 80 hp.
But how much power does it take to accelerate at 1 g at 100 mph. Your speed has doubled so the power has doubled: 160 hp.

So comparing the acceleration at 10 mph and 60 mph means comparing one condition with another that will require 6 times as much power - put another way: The same amount of power available at 10 mph and 60 mph will deliver 1/6th the acceleration.


Also I think the ecomodder calculator is wrong.
-mort

[sendler]

Originally Posted by mort

But the amount of power it takes to accelerate also depends on your speed.

True. That is why my last example with the trucks was a bad one. And my statement that 3rd would pull harder than 5th given the same speed and power with just a different rpm along the super flat power curve was wrong. The acceleration would be the same. The starting speed was the same in each example and so was the power being applied. And so was the rear wheel torque in either gear. More on this coming right up.
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Even though I was wrong in that statement, it helped me get back to the premise I am trying to prove.
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First gear accelerates at a much higher value than 6th. And not because of air resistance at speed in 6th.
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Because we are comparing changes in energy.
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Lets use horsepower hours for energy to keep the terms we have already been using. Or, horse power seconds to put into the appropriate scale. If I have to come up with exact equations for mass and speeds to support my point, I will. But I think we can get the idea from the concepts, without resorting to using exact numbers which will waste a lot of time to throw together.
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We have a CBR250R and the area under the power band we are using as we shift from the high side of the power peak to the low side with each gear is the same from 9,500 rpm to 7,500 and averages 20 hp. Let's say we start with 20 horse power seconds to begin with and 226kg at 6.7 meters/ second while cruising in 1st. So we pin the throttle while cruising at 7,500 rpm in 1st, 1 second later we have added 20hp seconds of energy to what ever we had before. Now we are up to 9.47 m/s and are carrying 40 hps. At the end of 2 seconds we will be carrying 60 hps and 11.6 m/s. We have doubled our energy vs the starting point in the first second and added another 33% to that in the second second. These are big changes of energy vs time. And big changes of speed vs time. So, a high acceleration. .276 G over the first second and .217 G over the second second. Now we continue to accelerate and shift up through the gears each time we reach 9.500 rpm until we hit 5th at the ten second mark. We now have 220 hp seconds of energy and 22.22 m/s. One more second later we have 240 hps and 23.21 m/s. We only gained 1 meter per second which is .1 G of acceleration. Less than half the acceleration we had between the first and second seconds of the run when the speed was low.
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This has nothing to do with wind yet which will indeed have a big effect on such a small amount of horsepower and acceleration. It is because the energy we are putting in is just increasing linearly with time but the speed is squared on it's side of the equation.
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And this brings me to the real revelation I had from the truck's dynos and 3rd accelerating the same as 5th. Power is the metric of how fast you can gain speed as I have been saying. And in the end, the torque multiplication of the different gears doesn't really do anything to make something pull harder other than to match the engine power band to the needed wheel speed.

[niky]

See... you're simply reading the dynos wrong.

Dynos interpolate engine torque by measuring the force at the wheels, then back-calculating engine torque by comparing wheel speed to engine speed.

Those readouts are not what the dyno is actually seeing, but the dyno's interpretation of the results, translated for the operator.

The raw numbers do not look anything like that. Raw wheel torque or force numbers plotted against road speed look like this:


Or translated into acceleration potential, thus:


So, yes... third gear should pull harder than fifth at any speed where the two gears intersect (unless you have a really weird powerband). If gearing had no multiplication effect, you would NOT be able to do a wheelie in first gear, no matter how hard you tried.

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Furthermore, I think you're confusing terminology in your example. What you're describing being built up as the bike goes down the road is momentum, which is

force(mass) x velocity

or

force(mass) x (distance / time)

Yet you're labeling it "horsepower per second", which is

(force(mass) x velocity) / time

or

force(mass) x distance / time2

Which isn't momentum.

It's best if you simply drop engine horsepower from the equation completely, and focus on wheel torque, which you can extrapolate from a dyno plot and gearing data. Seen this way, it's pretty obvious that it's not built up momentum that is slowing down acceleration, but decreasing wheel torque due to lower and lower gear multiplication at high speeds.

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If you use a rocket instead of a drive wheel and drive your bike in space, you will be able to maintain perfect acceleration no matter how much momentum you put into the bike.

Well, at least until you experience speed-of-light related relativistic effects... but basically, a build-up of momentum is NOT what is slowing down your acceleration here on Earth.

[sendler]

Nice post. I really appreciate having others who are not afraid to come out and play. It makes me think. This whole thing is an ongoing thought experiment for me which I have never worked through before and I will undoubtedly make mistakes along the way.

Originally Posted by niky

Raw wheel torque or force numbers plotted against road speed look like this:

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True. My point exactly. In all gears those lines will all show the same power at the wheel as the engine is sending out even though the torque is much higher in the lower gears, the wheel speed is much lower. It's a wash. The power at the wheel is the same in any gear.

Originally Posted by niky

Or translated into acceleration potential, thus:

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Yes. the acceleration inlower gears is always much greater than the higher gears because the speed is much lower. Hence, the energy of the vehicle is much lower. So any new energy that is added from the engine power is a big change. At faster speeds the energy of the vehicle can be 20 times, ect, what it was at the slower speed. But you are still only adding more energy from the same engine output 1 unit at a time. Now each time you look at it, you have increased the energy of the vehicle only 5%.
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Originally Posted by niky

So, yes... third gear should pull harder than fifth at any speed where the two gears intersect (unless you have a really weird powerband).

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Look at the dyno of the trucks again. They are modern turbo diesels and they do have a very weird, ultra flat power band. At any identical wheel speed where the gears have an rpm that is on the power band, say 3rd is 3,500, 4th is 3,000 and 5th is 2,500, The acceleration would be exactly the same. The gearing can't transform the power it is given. It only transforms the wheel speed to the engine speed.
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Originally Posted by niky

If gearing had no multiplication effect, you would NOT be able to do a wheelie in first gear, no matter how hard you tried.

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The torque is much higher in first so the so the action of rotating the front of the bike up and over is much stronger true. But the torque in and of itself does not accelerate the bike. Power accelerates the bike. which is again, much easier to change when you add more energy to a very small amount. A wheelie is also caused by the vicious change in the rate of acceleration. Jerk. Because the power is being applied to the road. Which is way below the cg of the vehicle. The bottom of the rear wheel is trying to drive right under the front of the vehicle and leave it behind.
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Originally Posted by niky

"horsepower per second"

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I'm not using horsepower per second. I am using horsepower times seconds. Which is energy. The same as a Watt hour or a Joule. Momentum is just one of many forms of energy.

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Originally Posted by niky

speed-of-light related relativistic effects

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Obviously my statements about energy increasing have nothing to do with the mass changing at these speeds. Only V squared is changing with more and more energy added.