Race cars - Torque vs Hp - The Undiscovered Country (for many)

rcgldr

Not quite:

4) deterimes the speed at the tire = surface of drum = radius times angular velocity.
5) determines the power by multplying force time speed (at the tire contact patch).

xxChrisxx

Both are actally correct :P, the last two steps manipulate the units in the same way. That just inculdes a time function at step 4 and not 5.

I prefer the way you said it though, I think its slightly more clear. So i'll steal your answer and edit my other post :D

zanick

Ok, we got a little side tracked on how power is measured on a dyno. I still think if you have the rate of change of the KE, cant you solve for acceleration and then work backward to find the force (and then easily convert to torque)? Going back to the linear world, if a car is accelerating at a certain rate, and we know two velocities, the mass of the car, doesnt average power=dw/dt ? It seems that we would have to calculate the change in work from the rate of change of KE. Kind of digging a hole here, I know. :)

Anyway, getting back to the original point and question, what would the terms used in comparing two same vehicles with equal HP "rated" engines, one being higher torque than the other, at different rpm ranges each? Im pointing at watt-seconds or HP-seconds to determine which one would yield the greatest rear wheel forces at any vehicle speed.
(gearing proportioal to each engines rpm range to achieve the same speed in any gear).
Integration of the rear wheel torque curves would obviously do this, but a succession of them would have to be used due to overlap. integrating the HP curves wouldnt do it either, as time spent in higher rpm ranges is different and would give incorrect weighted values for the results. I keep on falling back to HP-seconds or watt-secons as the answer, and Im really asking, in the physics world, what would be the best way to address this with the correct terminology. The car is an interesting subject, with varying force even if power was constant, but its not due to gearing and power varies as well. What I have found, is the easiest way to determine optimal acceleration is to look at the HP curves adjusted to the same vehicle speed operating ranges. Or, just look at gearing spacing, and use same percentage drop of each engine to determine the area that will be maximized and used under the HP curves. However, this doesnt adress the time factor, thats why it seems like HP-seconds is the right way to look at this to compare performance.
Same could be done for rear wheel torque figures, but would be a little more cumbersome to calculate.

It seems that comparing the shape of two HP curves, with the same proportioal engine rpm ranges is the easiest way to compare vehicle performance.*

Thoughts?

mk

*two engines, one with a 10,000rpm redline and the other 5,000rpm redline and shift points.
Both would have 25% rpm drops per shift per gear. Both engines have the same peak HP values, but would have different shaped curves or the same shaped curves, but either way, grossly different engine torque values.

xxChrisxx

You are refusing to budge from incorrect thinking and its very difficult to give a techincally correct explination until you do. You need to stop thinking about KE now, and start thinking about momentum if you want a technically correct explaination.

By simply using KE you are ignoring what the dyno is actually measuring. Therefore any further premise from that is based on false mathematics. You are approaching the problem backwards.

Just because you can maniplulate the equations the correct way on paper doesnt mean it is done like that in reality. Without a context energy means very little, and its the context that gives it importance.

What you are saying is correct for the car acceleration, but you are butching the way this is acutally calculated. Its also leading you to incorrect thinking. That more power is more force. This isnt correct and is also why you are getting the 1.5hp motor climing a hill messed up a bit.

More torque is more force, more power is force more quickly. (you cannot do this the other way around)
More power does not = more force.

Now for car acceleration, the rear wheel force (and by extansion engine torque) is larger than the drag forces. So for each torque operation you have a net positive force, so if you apply that more quickly you will accelerate more quickly.

For climbing a hill, the forces stopping the motion are much much higher. Its concevable that for a low powered (read low torque) motor, the torque will not provide the force to overcome the 'drag' forces at the rear wheel. You have a net negative force. Now no matter how often you apply this net negative force it will NEVER become positive and you will never climb the hill.

By your reasoning if you increase the power with the same engine (it spin it faster) you will be developing more power, but you will still never get up the hill.

This is the reason why trucks are so good at climbing hills with a full load, tons of torque. So they can climb steeper hills, but the low power means they wont do it quickly. If you hook up a formula 1 engine (same power or even lots more power rating but much lower torque) to the truck it wont have the pulling power to climb with several tons attached.

your battery/electric motor example. You say doubling the power will allow you to lift something heavier, this is true. But as they are operating at the same rpm, the way it doubles power is by doubling the torque outrput.

I'm going to come up with a worked example to show this.

zanick

ll concede that calcuating dyno force is really based on acceleration of the load and power is calculated from that. Again, not really the point of the discussion, but thanks, as I do want to stay on the accepted side of the explainations.

HOWEVER, your truck and the climbing hill example does not seem right. first of all , if you add more power to a mini bike climbing a hill, but failing, more hp will result in a higher force, as seen by power=fs. by adding NOS for example to that engine along with Fuel, we increase the power rating of the engine. Its rate of doing work is increased proportionally. If you just increase rpm, as you suggest, the mini bike would have to go faster up the hill, greatly increasing the force demands. however, if the engine rpm increased and the gearing allowed for the same equivilant speed, (and the engine HP curve was flat, or engine torque went down in proportion to rpm going up) then , you would be utilzing more of the available engine power and would be able to climb the hill. torque and force at the rear wheels would go up. By saying that just increasing the frequency or RPM a negative net force, makes no sense, as you would be changing the vehicle speed higher.
This is exactly why cars with gear boxes, downshift to climb hills at the same rate of speed. to take advantage of more available HP of the engine . rpm goes up, torque goes up at the rear wheels due to gearing and more hp is utilized.

With the truck vs the formula one engine, both can climb the hill at exactly the same rate if they have the same HP. Rate of doing work, right? the F1 engine does it by high rpm and low torque, the truck the opposite. in the end, if both are using the same HP, both will have the same rear wheel forces at an speed . The real reason that trucks use high torque, low rpm engines, is wear and efficiency. How long would a 15,000rpm engine last pulling a truck up a 100mile incline? The truck could do it for 100s of thousands of miles due to operating at very low rpm. The truck makes decent HP at very low rpm. very broad HP curve. the F1 engine is peaky and has a narrow max HP range.

I can easily give you resultant rear wheel torque to prove that any engine rated at the same hp, even at much less engine torque, will create the exact same rear wheel forces to the ground. Thats a simple set of equations. This seems to be in direct conflict it with your last sentence. This would be consistant with, "power=force x speed".

mk

xxChrisxx

Jesus.Power = force * speed is NOT based in reality.

It is a mathematical relation devised purely for convenience,

xxChrisxx

Jesus.Power = force * speed is NOT based in reality.

It is a mathematical relation devised purely for convenience, it shas no physical basis. im talking about the power part, not the force * speed.

By injecting nos you are increasing the engine TORQUE at a given rpm because you are increasing the force on the piston and by extension the power. NOT THE OTHER WAY ROUND.

To talk of gearing, why when you are coming to a hill do you downshift? If power is the key factor in rear wheel force it shoudlnt matter about the gear you are in as the engien is pumping out the same power. They downshift to take advantage of the TORQUE multiplication of the lower gear ratio. Seriesly do the calculations for the F1 and truck engine. I gaurantee you will make the mistake that power = force. IT DOESNT!!!!!!!!!!!!!

See how it works : http://auto.howstuffworks.com/question381.htm

^^ read it^^

You are really confusing yourself by flitting between the rear wheel horsepower and rear wheel torque. give all the equations you can.

you seem to clearly have problems thinking in terms of torque and power.

Seriously please go and buy a book on this. i'll have a look through my library for the best one.

zanick

ll concede that calcuating dyno force is really based on acceleration of the loads and power is calculated from that. again, not really the point of the discussion, but thanks, as I do want to stay on the accepted side of the explainations.

HOWEVER, you truck and climbing hill example does not seem right. first of all , if you add more power to a mini bike climbing a hill, but failing, more hp will relate in higher force, as seen by power=fs. by adding NOS for example to that engine along with Fuel, we increase the power rating of the engine. Its rate of doing work is increased proportionally. If you just increase rpm, as you suggest, the mini bike would have to go faster up the hill, greatly increasing the force demands. however, if the engine rpm increased and the gearing allowed for the same equivilant speed, (and the engine HP curve was flat, or engine torque went down in proportion to rpm going up) then , you would be utilzing more of the available engine power and would be able to climb the hill. torque and force at the rear wheels would go up. By saying that just increasing the frequency or RPM a negative net force, makes no sense, as you would be changing the vehicle speed higher.

you also say: "More torque is more force, more power is force more quickly. (you cannot do this the other way around)
More power does not = more force. But with power=fv, it does indicate that more power would create more force. (or to keep on the force side of thinking, a higher power rating would indicate that more force would have to be produced at the same vehicle speed to climb that hill.


Now for car acceleration, the rear wheel force (and by extansion engine torque) is larger than the drag forces. So for each torque operation you have a net positive force, so if you apply that more quickly you will accelerate more quickly."


With the truck vs the formula one engine, both can climb the hill at exactly the same rate if they have the same HP. Rate of doing work, right? the F1 engine does it by high rpm and low torque, the truck the opposite. in the end, if both are using the same HP, both will have the same rear wheel forces at an speed . The real reason that trucks use high torque, low rpm engines, is wear and efficiency. How long would a 15,000rpm engine last pulling a truck up a 100mile incline? The truck could do it for 100s of thousands of miles due to operating at very low rpm. The truck makes decent HP at very low rpm. very broad HP curve. the F1 engine is peaky and has a narrow max HP range.

I can easily give you resultant rear wheel torque to prove that any engine rated at the same hp, even at much less engine torque, will create the exact same rear wheel forces to the ground. Thats a simple set of equations. This seems to be in direct conflict it with your last sentence. This would be consistant with, "power=force x speed".

mk

xxChrisxx

You are pretty much wrong in everything you've just said regarding power.

Read the links on how stuff works, or go to your amazon and buy a book on this subject.

Until you realise your fundamental error in thinking you will never learn why you are going wrong. You are clinging to P=F*s, but if you'd acutrally read up on this you know that that relation is not what is heppening in reality. you will discorver its a mathemetical relation devised by people AFTER pissing about with torque and rpm and then doing lots of calculations to it for so long. You will also discover why its the torque that creates the force at the wheel NOT POWER.

Until then there is nothing I can do to increase your inderstanding of this.

zanick

I get what you are saying, especially with the NOS example. we get more torque, and subsequently more force at the rear wheels. I just have to change my direction of thinking. (coming from car land.)

But, when you talk of gearing below, you lose me. power is the key. you ask the question below. power is key and as you are crusing along at 50mph with your truck, you are using 100hp of your 800hp rating. Here comes the hill, you need much more force to climp the hill, you downshift to take advantage of the engines power available at the higher rpm and higher fuel requirements. At that prior power setting, you might have only been at 10% of the power available. now, you take advantage of higher gear reduction by downshifting, you now are in the higher rpm ranges and at the higher hp range at full throttle. You also are maximizing you rear wheel forces at the max HP range.

Now, you asked me to compare a high torque, low rpm truck engine and F1 engine at the same power, so here it is. Lets keep it simple. 1000hp 1000ft-lbs of peak torque for the truck and 1000hp and 250ft-lbs of peak torque for the F1 engine. The both go to climp a hill. The Big diesel engine is in the truck. At 50mph, the truck is at 4000rpm and producing 8000ft-lbs of torque at the rear wheels. (1000ft-lbs with 8:1 gearing) At the same 50mph, the truck with the F1 engine is running at 16,000rpm and 250ft-lbs of torque, but the rear wheel torque is the same 8000ft-lbs. (250ft-lbs with 32:1 gearing). vehicle speed is the same, HP is the same, engine torque is way different, yet, rear wheel forces are identical. Where is the mistake there?

mk

zanick

Im hearing you about that its really the force that determines the power, and power is just the power rating. But, you asked me to provide the example, and I did. Your truck powered by F1 or its normal engine, doesnt make your point, as i proved, both can yeild the same rear wheel torque at the same HP ratings, and grossly different engine torque values.
Power ratings is what you and I were comparing here and they seem to yield the same rear wheel torque at any vehicle speed. (if they are running at the same power level)

You mention i was wrong in "everything " i had a said regarding power. can you be more specific? you make the comparison of the truck powered by F1 engine vs its normal low reving high torque engine. that was actually incorrect. If power ratings are the same, the same rate of work can be done by either, and this means the same rear wheel torque can be produced!

In the electric motor and battery rating world, you get things rated in KW or KW-hours. unit measures of work. This indicates the potential rates of doing work. Is this wrong as well?

mk

xxChrisxx

You keep moving the goal posts by changing gearing. Gearing is a torque multiplyer.

He cannot change the gearing he has on his bike when he comes to a hill as he is geared for a certian road speed. For that gearing he doesnt have the RW torque available. When you said that he doesnt have the power available to do it, this is incorrect as the engine always produces the same power output, the phenomenon you are talking about is torque. The determination of whether you can climb the hill is torque, the determination of how fast you can climb is power. A rwhp value doesnt tell you if you can climb the hill or not, a rw force value would.

So to find if you can climb, you use:

RWTorque * wheel radius = Force

The RWHP tells you how fast you can climb it. from P = F * S

If you were theoretically detmining gearing before you set off to go this ans you had a RWHP curve, It would be correct to use P = F* S to determine the gearing for a set speed.

If you have set gearing available (ie you've already set off) The P = F* S does not tell you anything useful.
In this case you have to use RWT*wheel radius = F to determine if you have sufficient torque at the rear wheel to do the job. If you find that you dont you either have to go away and get the gearing that will give the correct RWT or you could slap bigger wheels on the bike. You can then find how fast you can climb the hill form P=T*angular velocity.

As jeff pointed out, he could climb that hill if he was geared for it. Then again with gears you can get any mortor to lift any amount. It'll jsut do it very slowly. So you see you can use the RWHP formula in some situations, but you can use the torque calculation in all situations.

What you were doing was the former, but applying it to the latter situation. So you were not calcualting anything useful. He stated he was geared for something already, and that it was his lack of torque that was causing the problem. Stating that he can do becuase P = F * S tells him he can is pointless as he cant chgane the gearing to get to the poitput that that equations states.

If you cannot climb a hill at the peak engine torque value, you cannot climb it at peak engine power. (as torque is lower at peak power). This transfers down through the transmission so that. If you can't climb a hill at peak RWT you cannot climb the hill at peak RWHP. It means you need to fiddle with the gearing to be able to do so. If you cant fiddle with the gearing and cant fit a larger wheel, you cant get up the hill. This is something that is easier to visualise using a torque calculation as that is the acutal physicla driving force.

I've got a question that i'm just finishing up that i'm going to post after your next reply. It should demonstrate that power is not the critical factor.

zanick

Not really, I think we are having the classis problem of rear wheel torque vs engine torque adding to the cross lines of the discussion. you tell me.

I think I see a potential problem. So, getting back to the mini bike. If he is running 1.5 hp and running some top speed say, 30mph, you are right. he has a certain amount of force being generated to sustain that speed. Stilll, power=force x speed. he is not at max torque of the engine, he is at max HP which as you say is higher than max torque of the engine. this is generating the maximum amount of force at that particular speed, 30mph. Now comes the hill. he cant choose a lower gear, because that would slow him down, so you are right. limied by max HP and rear wheel torque. if he adds NOS, it increases force by x% so he can climb the hill at that same speed.

You keep on saying that the bike cannont climb the hill if it doesnt have the torque, what you mean to say, is that if it was at max HP prior, and you wanted to keep the speed constant, yes that would be true. with more HP, you would have more force and then you would. you say its more force so then you can then determine the hp has increased as well. Thats fine. In the electrical /mechanical world, if i dropped in a higher output battery, to the elecrict motor powered bike, it could cause the motor to run with more torque and thus at a higher power level.

truck analogy with its stock engine vs F1 engine. If both engines are installed with appropriate gearing, both will be able to climb the hill at the same speed, using gears appropriate for the trade offs of rpm and speed and mulitplication of torque. One engine would do it at high rpm , low torque and the other would do it with high torque, low rpm. the net forces at the rear wheel would be the same because the rate of work would be the same.

Now , your last paragraph. If I have a transmission, and I cant climb a hill at a certain speed at max engine torque, there is a distinct possibilty, and in most cases, that i could climb it at max HP, even though the engine torque would be less at that same vehicle speed, rear wheel multiplied torque would be higher at that same vehicle speed than it would be found at max engine torque. agree? I think you two part sentence is saying that if you have a fixed gear, and you cant climb the hill at max torque, certanly at max HP you wouldnt be able to climb it, because the speed would be much higher. and your second part of the sentence, is saying that if you cant climb the hill with max rear wheel torque, as multipled thorugh the gear box at that speed, certainly you wouldnt be able to climb it at max hp, because those two points are the same engine rpm. max HP would be the point at which you would have max torque at any given speed. just like if we had an infinitely variable gear box, the engine would operate at max hp and not max torque to achieve max torque levels at the rear wheels at any given vehicle speed.






mk

xxChrisxx

Will repost q in a second.

Ok Q is:

14.4Kg block on a 45% slope

The motor used is:

100 Watt at 200rpm
4.77Nm at 200rpm

167.2 Watt at 400 rpm
4Nm at 400 rpm.

The reduction gearing is 15:1.
The rolling radius is 1m

Can the motor move the block up the hill?

EDIT: you can assume no losses through the drivetrain, so RWHP = engine HP.

Now after ansering this I'll give you the second part and address the truck and F1 engine thing.

Also buy this book :http://www.amazon.com/Four-Stroke-Pe...8802842&sr=8-1
and read the last chapter. It's not a very technical book, but is perfect for what we are talking about.

zanick

Well first off you have two motor speeds and thus driving speeds, fixed by a 15:1 gear box. If I cant change that, then I cant get speeds that utilize the available power of the motor.
the power range for the two speeds is 1:1.65, but the speed difference is 2x. so, I would need much more power to acheive 2x the speed of the 400rpm motor setting. If the slower motor setting works and uses all available power to lift the mass, even with optimal gearing, 1.67x greater power setting could only allow for a small increase in drive speed.

Thats at first glance. it looks like yes for the 100watt setting, but no for the 167watt setting due to the amount of power needed to raise the mass at 2x the speed.

xxChrisxx

First of all buy this book:
http://www.amazon.com/Four-Stroke-Pe...8802842&sr=8-1

And read the last chapter (hell you can read all of it if you want). It'll tell you exatly wehre your thinking is a bit off.


Regarding the question.

The acutal answer is neither will get it moving at that ratio.

Those are the peak figures, so the maximum power the motor can produce is 167.2 W. The maximum torque it can produce is 4.77 Nm.

The point of the above was to show that for a given gearing its the torque that creates the moving force. A minimum moving force requites a minimum torque at the wheels. The power figure has no bearing on this force. If it did the power figure would cause larger rear wheel forces and get it moving.

The next thing I was going to ask was try it with 21:1 (ive misplaces my notes on this i think that was the ratio). You'll find that the force at the wheel is then enough to move the block at the lower power figure but not the higher.

If you did rev it up (as more power apparently creates more force at the rear wheel) you should move faster. In fact it does the opposite, it you did rev it up you would no longer be providing enough force to overcome the resistance.

Do the acutal calucaltions and you'll see this is the case.


Here is my working for the 1st part:

14.4*9.81*cos(45)= 100N
You need at least 100N to get the block moving up the slope.

It can be shown that the rear wheel forces for each settign are:

100W setting.

Engine_Torque*gearing = Wheel torque.
4.77*15= 71.55 Nm at the wheel.
As the wheel is 1 m Rolling radius.
T=F*d
Force at wheel is 71.55 N

This gives a net negative force of 28.45N

for the higher power setting the wheel force (using the same method above is)
Force =60N

Using the power method: we know the power of the motor and the force necessary.

P=100W
F=100N

using P = F * S

100/100 = 1 m/s So to get the thing moving we need a wheel speed of 1m/s or below.

Wheel speed at lower power = circumfrence of wheel * angular velocity
for 1 second.

S = (2*pi)*(200/(15*60)) = 1.39 m/s
S = (2*pi)*(400/(15*60)) = 2.79 m/s

The wheel speeds are too high to provide the adequate forces to start the block moving.

So more power doesnt = more rear wheel force. And the torque method is fer better at this (its more clear that it wont work) as it is a snapshot in time.

rcgldr

It's not a fair comparason, setting the gearing for the same speed = 1.3963 m/s, with a radius of 1 meter:

100.00 watt at 200 rpm, 4.77465 Nm at 200 rpm, reduction gearing 15:1, force = 71.620 N
167.55 watt at 400 rpm, 4.00000 Nm at 400 rpm, reduction gearing 30:1, force = 120.00 N

As expected, 120.00 / 71.62 = 1.6755 = 167.55 / 100.00