Another torque versus horsepower question for a track car
01-02-2008, 12:39 AM
#91
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So you are saying that acceleration (measured in distance/time-squared) at a POINT IN TIME is at its highest value at the point of MAX HP and NOT at the point of MAX Torque? If you say yes this makes no sense to me at all. HP is a derived number based on torque and RPM. Acceleration, at a point in time, is essentially a measurement of how fast is the rotational motion of the wheels INCREASING (since that essentially maps to linear distance on the road..assuming no slippage). I don't care if you are going 10 mph or 100 mph or how fast the wheel rotation is (again assume no slippage)..acceleration is only measuring the "rate of increase" of that rotation. The ONLY measurement that affects the "rate of increase" in rotation is Torque...not HP...because, as a measurement it is derived from Torque.
01-02-2008, 01:00 AM
#92
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Torque at the wheel determines how quickly a car accelerate... which is not the same as torque at the crank.
If one engine makes 100lb/ft at 2600 rpm, the other makes 50lb/ft at 5200 rpm. (i.e. both engines makes ~50hp) The second car will accelerate as quickly if it has gears 50% shorter than the first car, since they will have the same torque available at the wheels.
Now if the second engine engine makes 60lb/ft at 5200rpm (ie. it makes ~60hp), the same 50% shorter gears will deliver more torque to the wheels, and help the car accelerate faster.
If one engine makes 100lb/ft at 2600 rpm, the other makes 50lb/ft at 5200 rpm. (i.e. both engines makes ~50hp) The second car will accelerate as quickly if it has gears 50% shorter than the first car, since they will have the same torque available at the wheels.
Now if the second engine engine makes 60lb/ft at 5200rpm (ie. it makes ~60hp), the same 50% shorter gears will deliver more torque to the wheels, and help the car accelerate faster.
01-02-2008, 01:02 AM
#93
Rennlist Member
This is why I get into these discussions. Acceleration is proportional to power.
Its not derived, but a is a rate of doing work. Its a rate of change of kinetic energy. I dont want to get philosophical, but we all know torque is a major component of HP. (equal only to that of RPM).
The problem, is folks get caught up in the "max torque" term. what we really want to determine, is the torque at the rear wheels at any vehicle speed. this is determined by HP. equal HP at any vehicle speed, between two cars, and they will accelerate the same, regardess of torque values.
acceleration is change of speed, you are correct. And this is determined by torque acting on the rear tires. However, the max acceleration rate that a vehicle can achieve, at any particular speed, is at its max HP. since we are limited to achieving this , because of the number of gear ratios we have to choose from, i always make it very clear, that we want to get as close to max HP as possible to maximize acceleration at any vehicle speed.
A clear example of this would be a vehicle traveling at max torque rpms and the resultant vehicle speed. say its 50mph. the hp level at max torque for most cars is some fraction of max HP. if you can downshift to a lower gear, and be close to the max HP levels, you will have more torque to the rear wheels, even though the engine torque levels is less. why??
acceleration = power/(mass x velocity)
max torque might be something like 200hp and max HP would be at 300hp. However, the torque available to the rear wheels would be proportionally greater as well.
Is that more clear?
MK
Its not derived, but a is a rate of doing work. Its a rate of change of kinetic energy. I dont want to get philosophical, but we all know torque is a major component of HP. (equal only to that of RPM).
The problem, is folks get caught up in the "max torque" term. what we really want to determine, is the torque at the rear wheels at any vehicle speed. this is determined by HP. equal HP at any vehicle speed, between two cars, and they will accelerate the same, regardess of torque values.
acceleration is change of speed, you are correct. And this is determined by torque acting on the rear tires. However, the max acceleration rate that a vehicle can achieve, at any particular speed, is at its max HP. since we are limited to achieving this , because of the number of gear ratios we have to choose from, i always make it very clear, that we want to get as close to max HP as possible to maximize acceleration at any vehicle speed.
A clear example of this would be a vehicle traveling at max torque rpms and the resultant vehicle speed. say its 50mph. the hp level at max torque for most cars is some fraction of max HP. if you can downshift to a lower gear, and be close to the max HP levels, you will have more torque to the rear wheels, even though the engine torque levels is less. why??
acceleration = power/(mass x velocity)
max torque might be something like 200hp and max HP would be at 300hp. However, the torque available to the rear wheels would be proportionally greater as well.
Is that more clear?
MK
So you are saying that acceleration (measured in distance/time-squared) at a POINT IN TIME is at its highest value at the point of MAX HP and NOT at the point of MAX Torque? If you say yes this makes no sense to me at all. HP is a derived number based on torque and RPM. Acceleration, at a point in time, is essentially a measurement of how fast is the rotational motion of the wheels INCREASING (since that essentially maps to linear distance on the road..assuming no slippage). I don't care if you are going 10 mph or 100 mph or how fast the wheel rotation is (again assume no slippage)..acceleration is only measuring the "rate of increase" of that rotation. The ONLY measurement that affects the "rate of increase" in rotation is Torque...not HP...because, as a measurement it is derived from Torque.
01-02-2008, 01:50 AM
#94
Rennlist Member
So, found the US 95 M3 curves.
Looks like redline was near 7000rpm and peak torque was at 4300. max torque as 210 and max HP near 6200rpm, and very flat from 5600 to 7000rpm. If a gear shift is .72 rpm drop, then if the torque at 7000rpm is a low 165ft-lbs, and near 220hp, this will produce much more HP and rear wheel torque, than if you were in a taller gear running at near max torque (near 5000rpm where HP is 200 and torque is as I mentioned, near 210ft-lbs) In fact, the difference is 10% and thats the difference in the torque at the rear wheels comparing the two gears available.
The net net of it all, is that you can run at max hp or on the way to max HP and your gains are exactly the same as the differences in HP at the two different rpms caused by a gear shift. If you know your gear spacing , looking at a HP curve makes it easy to see where you will have the most amount of rear wheel torque available. Looking at a torque curve, is much tougher, if not impossible, unless you got a calculator and all the gear ratios handy.
so, your US 3.0 M3 will always have more rear wheel torque available at any rpm, by maximizing HP and shifting at or near max RPMs. In otherwords, there is no point on the US M3 3.0L HP curve where a .71% rpm drop allows for any greater HP, and thats what we are talking about here. This is also true for the M3 euro 3.2 engines too. IN fact, i have only seen a few where this is possible. It would have to be an arc that is more narrow than the gear spacing, and thats REAL peaky
mk
Looks like redline was near 7000rpm and peak torque was at 4300. max torque as 210 and max HP near 6200rpm, and very flat from 5600 to 7000rpm. If a gear shift is .72 rpm drop, then if the torque at 7000rpm is a low 165ft-lbs, and near 220hp, this will produce much more HP and rear wheel torque, than if you were in a taller gear running at near max torque (near 5000rpm where HP is 200 and torque is as I mentioned, near 210ft-lbs) In fact, the difference is 10% and thats the difference in the torque at the rear wheels comparing the two gears available.
The net net of it all, is that you can run at max hp or on the way to max HP and your gains are exactly the same as the differences in HP at the two different rpms caused by a gear shift. If you know your gear spacing , looking at a HP curve makes it easy to see where you will have the most amount of rear wheel torque available. Looking at a torque curve, is much tougher, if not impossible, unless you got a calculator and all the gear ratios handy.
so, your US 3.0 M3 will always have more rear wheel torque available at any rpm, by maximizing HP and shifting at or near max RPMs. In otherwords, there is no point on the US M3 3.0L HP curve where a .71% rpm drop allows for any greater HP, and thats what we are talking about here. This is also true for the M3 euro 3.2 engines too. IN fact, i have only seen a few where this is possible. It would have to be an arc that is more narrow than the gear spacing, and thats REAL peaky
mk
Mark, I disagree. This all depends on the characteristics of the motor. As an example, let's look at 2 BMW's. E36 M3, in US spec, makes great torque from ~3000 rpm, and also makes good HP...but above around 6300 on the way to redline at 7000 to 7200 (depending on chip), it mostly makes noise. So it really does nto make sense to keep the car at redline, and works better to use the torque as much as possible. E46 330i, which I have raced professionally, makes less torque, and has a lower redline, which is a lot better aligned with the power peak. Thus, it makes more sense to keep the RPMs high.
01-02-2008, 08:04 AM
#95
OK, lets use an example that I can understand...
Here are my dino runs after opening the exhaust & intake a little on my otherwise stock
3.0 L 944 S2.
I have believed that it is best in this car to shift at 6000 RPM in order to keep the car in it's best power band (whatever that may be). It seems to me that the HP gains above that are negligible and the higher I go the more the torque drops off. My car drops about 1000RPM's between shifts.
Am I right or do I neeed to run it to redline or shift earlier??
Here are my dino runs after opening the exhaust & intake a little on my otherwise stock
3.0 L 944 S2.I have believed that it is best in this car to shift at 6000 RPM in order to keep the car in it's best power band (whatever that may be). It seems to me that the HP gains above that are negligible and the higher I go the more the torque drops off. My car drops about 1000RPM's between shifts.
Am I right or do I neeed to run it to redline or shift earlier??
01-02-2008, 10:45 AM
#96
Rennlist Member
Mark, I was actually using the US 3.2 liter OBD2 motor as my example, because it was much fatter lower down in the torque range and much worse at higher RPM's than the 3.0, which breathed pretty well up high & was better run near redline.
01-02-2008, 11:29 AM
#97
Race Director
Guys
HP = Torque * Engine speed. So in they are really the same thing. Mark is correct in that engine HP is what makes the car move not engine torque. It is torque at rear wheels, but that is completely adjust by gearing. So what do you want hp or torque? Well that depends on the POWERBAND. High hp motors with little peak torque tend to have narrow powerbands. The S2000 for example may make 240 hp, but that is peak hp. How much hp does it make over the usable rev range on track. Big torque motors may not make as much peak hp, but if they make more hp over the usable rev range they will appear to be faster out of a corner when the revs are low. Once the revs pick up the "peak" hp of the low torque car will tend to make it seem to surge on the big torque car. This where the entire area under the curve thing comes into play. Given the stock gearing my 944 spec car runs from about 4000 rpm to 6000 rpm. That is its effective rev range on track. I don't need torque below 4000 RPM, but I sure want it at 4000 RPM since more torque = more hp. I would rather have motor that has 132 hp peak at 5800 rpm vs a 138 peak at 6000 rpm if I can get 5 hp more from 4000 to 5500 rpm. The reason is that in an acceleration from 4000 to 6000 rpm I will be winning for the first 1500 rpm and that is much more time than I would be losing out from 5500 to 6000 rpm. Plus starting in an even 4000 RPM drag race if I have a bit more hp over that range then I will get to 5500 rpm sooner so that when the other guys his is power advnatage at 5500 rpm I maybe a 5700 rpm and this due to RPM alone may be even on hp just because I have more revs at the same point in time.
Now racing in traffic is even more critical as you tend to not beable to run clean accelrations and often are not in the idea spot on your rev range. So again cutting off the peak hp to get more hp in your rev range is a benefit. The big exception are long high speed straights where you may speed 10 sconds in top gear running near redline. Then that lack of top end power can be costly.
In the end you need hp make the car move since hp is measure of work and torque is just a force.
HP = Torque * Engine speed. So in they are really the same thing. Mark is correct in that engine HP is what makes the car move not engine torque. It is torque at rear wheels, but that is completely adjust by gearing. So what do you want hp or torque? Well that depends on the POWERBAND. High hp motors with little peak torque tend to have narrow powerbands. The S2000 for example may make 240 hp, but that is peak hp. How much hp does it make over the usable rev range on track. Big torque motors may not make as much peak hp, but if they make more hp over the usable rev range they will appear to be faster out of a corner when the revs are low. Once the revs pick up the "peak" hp of the low torque car will tend to make it seem to surge on the big torque car. This where the entire area under the curve thing comes into play. Given the stock gearing my 944 spec car runs from about 4000 rpm to 6000 rpm. That is its effective rev range on track. I don't need torque below 4000 RPM, but I sure want it at 4000 RPM since more torque = more hp. I would rather have motor that has 132 hp peak at 5800 rpm vs a 138 peak at 6000 rpm if I can get 5 hp more from 4000 to 5500 rpm. The reason is that in an acceleration from 4000 to 6000 rpm I will be winning for the first 1500 rpm and that is much more time than I would be losing out from 5500 to 6000 rpm. Plus starting in an even 4000 RPM drag race if I have a bit more hp over that range then I will get to 5500 rpm sooner so that when the other guys his is power advnatage at 5500 rpm I maybe a 5700 rpm and this due to RPM alone may be even on hp just because I have more revs at the same point in time.
Now racing in traffic is even more critical as you tend to not beable to run clean accelrations and often are not in the idea spot on your rev range. So again cutting off the peak hp to get more hp in your rev range is a benefit. The big exception are long high speed straights where you may speed 10 sconds in top gear running near redline. Then that lack of top end power can be costly.
In the end you need hp make the car move since hp is measure of work and torque is just a force.
01-02-2008, 11:55 AM
#98
So you are saying that acceleration (measured in distance/time-squared) at a POINT IN TIME is at its highest value at the point of MAX HP and NOT at the point of MAX Torque? If you say yes this makes no sense to me at all. HP is a derived number based on torque and RPM. Acceleration, at a point in time, is essentially a measurement of how fast is the rotational motion of the wheels INCREASING (since that essentially maps to linear distance on the road..assuming no slippage). I don't care if you are going 10 mph or 100 mph or how fast the wheel rotation is (again assume no slippage)..acceleration is only measuring the "rate of increase" of that rotation. The ONLY measurement that affects the "rate of increase" in rotation is Torque...not HP...because, as a measurement it is derived from Torque.
Here we have the HP curves overlayed w/ the thrust curves
It can be seen that the engine hp curves are always the same height but are stretched horizontally because more time is spent in each gear
As always the thrust curve also has the same shape though at a lower level in each gear. Thrust varies w/ the overall gear ratio.
The question always comes up, "What's the best shift point to maximize acceleration"
answer shift to maximize thrust in the next gear consistent w/ preserving engine life.
Here we have the HP & thrust curves for 1st and 2nd, note that shifting at 7K puts you in the fat part of the thrust curve for 2nd.
01-02-2008, 12:06 PM
#99
correct
correct, w/ the proviso that the rpm of max engine torque will still be the rpm of max wheel torque. A gear is just a simple machine, all it can do is trade speed or distance for force, in this case the engine spins faster(flywheel rpm) and whatever flywheel toque there is gets multiplied by the gear ratio to get more torque at the wheel but traveling proportionately slower(wheel rpm)
some convienient but unrealistic #s
engine 9000 rpm 200 ft-lb
3:1 gear
wheel 3000 rpm 600 ft-lb
correct, w/ the proviso that the rpm of max engine torque will still be the rpm of max wheel torque. A gear is just a simple machine, all it can do is trade speed or distance for force, in this case the engine spins faster(flywheel rpm) and whatever flywheel toque there is gets multiplied by the gear ratio to get more torque at the wheel but traveling proportionately slower(wheel rpm)
some convienient but unrealistic #s
engine 9000 rpm 200 ft-lb
3:1 gear
wheel 3000 rpm 600 ft-lb
01-02-2008, 02:11 PM
#100
Rennlist Member
Eddie, you can thank me for saving you a second a lap later
First of all, if you have only 1000rpm drop, shifting at 6000pm would be fine as you do have a pretty flat HP curve.(looks good)
But, its not "rpm drop" related. its pecentage related. take a look at your gear ratios and they are probably like the spacing on a 928 or BMW, meaning its near 72% rpm drop for a shift. that being the case, a shift at 6500rpm brings the rpms down to 4500rpm. a very quick calculation to see if you are maximizing your HP applied (ie HP-seconds), is to take 3 data points to get an average as long as the data points are fairly evenly spaced. you can see that the two data points up top will be close to your max HP, but as you short shift, the lower rpm data point brings down the average with a weight of about 1/3 the total. For your HP curve, its not much of a sacrafice, due to the torque/hp hump down near the 4500rpm range. Its not a huge difference for you HP curves, but in racing, it all helps.
the point of all this is to understand the difference between engine torque and HP and how it relates to the accelerative forces on your car. (not engine preservation that all of us consider)
Mk
First of all, if you have only 1000rpm drop, shifting at 6000pm would be fine as you do have a pretty flat HP curve.(looks good)
But, its not "rpm drop" related. its pecentage related. take a look at your gear ratios and they are probably like the spacing on a 928 or BMW, meaning its near 72% rpm drop for a shift. that being the case, a shift at 6500rpm brings the rpms down to 4500rpm. a very quick calculation to see if you are maximizing your HP applied (ie HP-seconds), is to take 3 data points to get an average as long as the data points are fairly evenly spaced. you can see that the two data points up top will be close to your max HP, but as you short shift, the lower rpm data point brings down the average with a weight of about 1/3 the total. For your HP curve, its not much of a sacrafice, due to the torque/hp hump down near the 4500rpm range. Its not a huge difference for you HP curves, but in racing, it all helps.
the point of all this is to understand the difference between engine torque and HP and how it relates to the accelerative forces on your car. (not engine preservation that all of us consider)
Mk
OK, lets use an example that I can understand...
Here are my dino runs after opening the exhaust & intake a little on my otherwise stock 3.0 L 944 S2.
I have believed that it is best in this car to shift at 6000 RPM in order to keep the car in it's best power band (whatever that may be). It seems to me that the HP gains above that are negligible and the higher I go the more the torque drops off. My car drops about 1000RPM's between shifts.
Am I right or do I neeed to run it to redline or shift earlier??
Here are my dino runs after opening the exhaust & intake a little on my otherwise stock
3.0 L 944 S2.I have believed that it is best in this car to shift at 6000 RPM in order to keep the car in it's best power band (whatever that may be). It seems to me that the HP gains above that are negligible and the higher I go the more the torque drops off. My car drops about 1000RPM's between shifts.
Am I right or do I neeed to run it to redline or shift earlier??
01-02-2008, 02:18 PM
#101
Rennlist Member
ok, even with the 3.2, the curves are such that there is no point in short shifting, unless you want to be slower
take a look at them yourself and see if there is at any point, a greater hp by shifting short of redline. Here are two curves of the same 3.2 euro motor. the better hp curve, is due to an air box change.
so, can you find any point on the curve where it shows it makes sense to short shift?
whats nice about these curves is that there is a flat table HP curve. If it was flat for any longer it would have the effect of a CVT!
(meaning, HP would be constant and this would maximize HP) so, the only thing you sacrafice by short shifting here is the 1st data point if we use the 3 point averaging method. by short shifting by 500rpm, you loose near 25hp on the first data point. Since its value is about 1/3 the total Hp-seconds, you can see that a short shift could cost near 8hp overall. (very rough estimation, but you get the point)
You also spend less time at the top hp level, but that goes back to the HP-seconds concept.
Mk
take a look at them yourself and see if there is at any point, a greater hp by shifting short of redline. Here are two curves of the same 3.2 euro motor. the better hp curve, is due to an air box change.
so, can you find any point on the curve where it shows it makes sense to short shift?
whats nice about these curves is that there is a flat table HP curve. If it was flat for any longer it would have the effect of a CVT!
(meaning, HP would be constant and this would maximize HP) so, the only thing you sacrafice by short shifting here is the 1st data point if we use the 3 point averaging method. by short shifting by 500rpm, you loose near 25hp on the first data point. Since its value is about 1/3 the total Hp-seconds, you can see that a short shift could cost near 8hp overall. (very rough estimation, but you get the point)
You also spend less time at the top hp level, but that goes back to the HP-seconds concept.
Mk
Last edited by mark kibort; 01-02-2008 at 02:36 PM.
01-02-2008, 02:51 PM
#102
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OK Gang (and Mark K.)…here is my shot at it….please have at it.
Acceleration is NOT function of power. It is a function of force. Power is derived from force but this does not make acceleration a function of power directly. To look at the the equation ACCELERATION = POWER/(MASS * VELOCITY) and thus conclude ACCELERATION IS A FUNCTION OF POWER is an incorrect interpretation of this equation. This is NOT, in fact, what that equation is saying. I will get to that in a moment. But first some basic postulates:
1. The acceleration we are talking about is the instantaneous G-force experienced by the car. We are not talking about a 0-60 time…this is an AVERAGE acceleration. Making the statement that max acceleration occurs AT MAX. HP infers we are talking about instantaneous acceleration experienced at some point on the RPM curve, I just want to make sure we are on the same page of how we define acceleration.
2. I am saying that the acceleration experienced by a car is a function of one thing only…Torque. Assuming, of course, that friction, air resistance, etc. are ignored. We are speaking only of engine performance as characterized by a “dyno” curve.
3. Therefore if you placed an accelerometer into a car and measured its reading through a WOT acceleration and the engine performed exactly as it did on the dyno (ie. leave it in the same gear), then the profile of the acceleration readings experienced by the car would THEORECTICALLY be identical to the profile of the TORQUE curve from the dyno and not the HP curve. IE. the maximum value for the g-force (acceleration) would be at the rpm where the MAX torque was read by the dyno and NOT at the RPM where the max HP was recorded (again…theoretically).
First, let’s look at the correct physics.
Acceleration = Force/Mass. (F = ma), it gets no simpler than that.
Where:
a = acceleration of the car
m = mass of the car
F = the force applied to the car in order to induce the acceleration.
There is only one force that a car experiences that is generated by the engine…torque. It does not experience HP, that is a derived quantity. In general terms Torque = Force X Distance (T = Fd). It is a unit of energy (I am using T for torque here). In this case and in very simple terms the “distance” is the radius point of the rotation at which the force is measured. This is important to understand because we are not talking about the speed or velocity of the car…but the rotational speed at the point we area measuring the force on the rotation shaft to come up with our torque number. They are certainly related by the gearing...but the whole issue of gears confuses this discussion because we can actually ignore the gears altogether. We are not talking about absolute acceleration, but the relative acceleration over the functional RPM range of the engine. Pick any gear you want….just don’t change it during the test. This acceleration is being induced at the point where the "rubber meets the road". That is where it is measured...everything from there back to the engine is just a bunch of gears.
So with the above we can simplify F=ma even further to a = T/(md). Assuming that the mass of the car is constant and that the gear is not changed during the measurement then acceleration is a function of Torque (T) ONLY. Its as simple as that.
So back to our ACCELERATION = POWER/(MASS*VELOCITY) or to shorten:
a = P/(mv)
To say that acceleration varies according to power is an incorrect representation of this equation. This equation, in fact, COMPLETELY supports the fact that acceleration varies as a function of torque only. How?
It’s the pesky little “velocity” term. In order for acceleration to vary ACCORDING to power, it requires that all variables on the right hand side of the equation be kept constant and that power is then varied and the resulting change in acceleration is then measured. ONLY ONE PROBLEM….you cannot keep the other terms constant in order for the equation to be meaningful. The “velocity” in the denominator is the same "velocity" that is in the “POWER” term (remember P=Force X Velocity)) The acceleration is independent of the velocity term since it cancels out and you are left with….wait for it…torque. You want the math…here it is:
Power = Torque/time = force X (distance/time)
V = distance/time
m=mass
acceleration=distance/(time squared)
Everything cancels out and you are left with a = F/m, assuming the distance is kept constant (no change in gears) and we have shown that the time changes (ie. RPM increase) cancel out, the only dependent variables are mass and force...and since the mass is constant...the only dependent variable is Force and thus Torque.
In order for the equation a=P/(mv) to work the “distance” and “time” of the power (P) term and the velocity (v) term must be measuring the same thing. Therefore acceleration is NOT, BY DEFINTION dependent on Power...only Torque.
It would take too long to do here but you can see that one can manipulate these equations to increase power and keep acceleration constant, one can decrease power and increase acceleration...there is no direct relationship to power.
The ONLY way the acceleration vs. power interpretation of the equation works is if the “velocity” term in the denominator is independent of power. However, one quick look (beyond the math) shows why this is absurd. Let us say that it is independent and we can therefore hold the Power and the mass terms constant. As we decrease “velocity” the acceleration tends towards infinity. This is clearly wrong.
So the g-force (acceleration) experience by a moving vehicle at a given point of the RPM curve is a function only of the torque generated by the engine for a given gear, and thus MAX g-force (acceleration) is experienced at MAX torque...not MAX HP.
(Did an edit for clarity)
Acceleration is NOT function of power. It is a function of force. Power is derived from force but this does not make acceleration a function of power directly. To look at the the equation ACCELERATION = POWER/(MASS * VELOCITY) and thus conclude ACCELERATION IS A FUNCTION OF POWER is an incorrect interpretation of this equation. This is NOT, in fact, what that equation is saying. I will get to that in a moment. But first some basic postulates:
1. The acceleration we are talking about is the instantaneous G-force experienced by the car. We are not talking about a 0-60 time…this is an AVERAGE acceleration. Making the statement that max acceleration occurs AT MAX. HP infers we are talking about instantaneous acceleration experienced at some point on the RPM curve, I just want to make sure we are on the same page of how we define acceleration.
2. I am saying that the acceleration experienced by a car is a function of one thing only…Torque. Assuming, of course, that friction, air resistance, etc. are ignored. We are speaking only of engine performance as characterized by a “dyno” curve.
3. Therefore if you placed an accelerometer into a car and measured its reading through a WOT acceleration and the engine performed exactly as it did on the dyno (ie. leave it in the same gear), then the profile of the acceleration readings experienced by the car would THEORECTICALLY be identical to the profile of the TORQUE curve from the dyno and not the HP curve. IE. the maximum value for the g-force (acceleration) would be at the rpm where the MAX torque was read by the dyno and NOT at the RPM where the max HP was recorded (again…theoretically).
First, let’s look at the correct physics.
Acceleration = Force/Mass. (F = ma), it gets no simpler than that.
Where:
a = acceleration of the car
m = mass of the car
F = the force applied to the car in order to induce the acceleration.
There is only one force that a car experiences that is generated by the engine…torque. It does not experience HP, that is a derived quantity. In general terms Torque = Force X Distance (T = Fd). It is a unit of energy (I am using T for torque here). In this case and in very simple terms the “distance” is the radius point of the rotation at which the force is measured. This is important to understand because we are not talking about the speed or velocity of the car…but the rotational speed at the point we area measuring the force on the rotation shaft to come up with our torque number. They are certainly related by the gearing...but the whole issue of gears confuses this discussion because we can actually ignore the gears altogether. We are not talking about absolute acceleration, but the relative acceleration over the functional RPM range of the engine. Pick any gear you want….just don’t change it during the test. This acceleration is being induced at the point where the "rubber meets the road". That is where it is measured...everything from there back to the engine is just a bunch of gears.
So with the above we can simplify F=ma even further to a = T/(md). Assuming that the mass of the car is constant and that the gear is not changed during the measurement then acceleration is a function of Torque (T) ONLY. Its as simple as that.
So back to our ACCELERATION = POWER/(MASS*VELOCITY) or to shorten:
a = P/(mv)
To say that acceleration varies according to power is an incorrect representation of this equation. This equation, in fact, COMPLETELY supports the fact that acceleration varies as a function of torque only. How?
It’s the pesky little “velocity” term. In order for acceleration to vary ACCORDING to power, it requires that all variables on the right hand side of the equation be kept constant and that power is then varied and the resulting change in acceleration is then measured. ONLY ONE PROBLEM….you cannot keep the other terms constant in order for the equation to be meaningful. The “velocity” in the denominator is the same "velocity" that is in the “POWER” term (remember P=Force X Velocity)) The acceleration is independent of the velocity term since it cancels out and you are left with….wait for it…torque. You want the math…here it is:
Power = Torque/time = force X (distance/time)
V = distance/time
m=mass
acceleration=distance/(time squared)
Everything cancels out and you are left with a = F/m, assuming the distance is kept constant (no change in gears) and we have shown that the time changes (ie. RPM increase) cancel out, the only dependent variables are mass and force...and since the mass is constant...the only dependent variable is Force and thus Torque.
In order for the equation a=P/(mv) to work the “distance” and “time” of the power (P) term and the velocity (v) term must be measuring the same thing. Therefore acceleration is NOT, BY DEFINTION dependent on Power...only Torque.
It would take too long to do here but you can see that one can manipulate these equations to increase power and keep acceleration constant, one can decrease power and increase acceleration...there is no direct relationship to power.
The ONLY way the acceleration vs. power interpretation of the equation works is if the “velocity” term in the denominator is independent of power. However, one quick look (beyond the math) shows why this is absurd. Let us say that it is independent and we can therefore hold the Power and the mass terms constant. As we decrease “velocity” the acceleration tends towards infinity. This is clearly wrong.
So the g-force (acceleration) experience by a moving vehicle at a given point of the RPM curve is a function only of the torque generated by the engine for a given gear, and thus MAX g-force (acceleration) is experienced at MAX torque...not MAX HP.
(Did an edit for clarity)
Last edited by DaveM993; 01-02-2008 at 03:27 PM.
01-02-2008, 03:25 PM
#103
Rennlist Member
Mark, those graphs are not a stock motor. The stock motor made 240 crank HP and 240 crank lb-ft of torque. You are showing RWHP & RWTQ numbers WAYYYYYYY above that.
What you are showing is a heavily modified motor making a LOT more HP & TQ, with curves that do not reflect a stock motor & the stock motor's characteristics.
What you are showing is a heavily modified motor making a LOT more HP & TQ, with curves that do not reflect a stock motor & the stock motor's characteristics.
01-02-2008, 03:50 PM
#104
Rennlist Member
your right, its a euro 3.2. I dont have the US 3.2 curves, but did quote the US 3.0 curves. It really doesnt matter. Just look at your HP curves and see, based on the spread of your gear shifts , like i said, its about 72% drop, and see if it pays to shift early. in 95% of the time, it wont. for this to happen, you really need one of those bell shapped HP curves that peak at 6000rpm and fall dramatcially to a much lower HP at 7000rpm than the post shift point of 5000rpm. If this happens, you would need to shift at a point equal to the HP level of the post shift, where the hp would be climbing with increased RPM.
thats about as clear as i can make it. let me know if that makes sense.
MK
thats about as clear as i can make it. let me know if that makes sense.
MK
Mark, those graphs are not a stock motor. The stock motor made 240 crank HP and 240 crank lb-ft of torque. You are showing RWHP & RWTQ numbers WAYYYYYYY above that.
What you are showing is a heavily modified motor making a LOT more HP & TQ, with curves that do not reflect a stock motor & the stock motor's characteristics.
What you are showing is a heavily modified motor making a LOT more HP & TQ, with curves that do not reflect a stock motor & the stock motor's characteristics.
01-02-2008, 03:57 PM
#105
Rennlist Member
All I know is that, in real life, on real life technical tracks (like Motorsport Ranch), I am ~2 seconds a lap faster when I use more of my beefy torque, and less of the wheezy 7,000 RPM redline.