Effect of weight during highway pulls?
09-29-04, 11:56 AM
#26
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Originally Posted by jimlab
Newton's second law is "real world" also. Let's review it...
F = M * A
For our purposes, it is best to rearrange the equation in terms of acceleration.
A = F / M
Acceleration is directly proportional to force. If you push an object twice as hard, it will accelerate twice as fast, assuming mass remains constant.
Acceleration is inversely proportional to mass. If you double the weight, the object accelerates half as fast with the same force.
At higher speeds, I have proven that Force at the wheels decreases, due to gearing, air, and rolling resistance. As Force decreases, so must acceleration. Mass, however, remains a constant.
As Newton's equation shows, Mass actually has an increasing effect at higher speed where Force is decreasing. Reducing Force has the same effect as increasing Mass; acceleration decreases.
How about a few CarTest 2000 numbers where weight is the only change to back this up?
0-30 mph
2,800 lb. FD, stock engine - 1.93 sec.
3,300 lb. FD, stock engine - 2.15 sec. (+0.22 sec., +11%)
3,800 lb. FD, stock engine - 2.36 sec. (+0.43 sec., +22%)
100-130 mph
2,800 lb. FD, stock engine, 4th gear start - 10.31 sec.
3,300 lb. FD, stock engine, 4th gear start - 12.24 sec. (+1.93 sec., +18%)
3,800 lb. FD, stock engine, 4th gear start - 14.36 sec. (+4.05 sec., +39%)
If weight had less of an effect at high speed, you would expect the variance between the 100-130 acceleration times to be less than the 0-30 times, but it isn't. The variance is actually significantly higher. Obviously Mass has even more affect at higher speeds.
I know it seems like weight would have less of an effect at higher speed, once the chore of getting the car into motion is over, but that is not the case. That is simply something Supra owners tell themselves to feel better about having to have far more power to accelerate as quickly as an FD owner can with less. Their gearing and the fact that they can make more power is their only advantage.
F = M * A
For our purposes, it is best to rearrange the equation in terms of acceleration.
A = F / M
Acceleration is directly proportional to force. If you push an object twice as hard, it will accelerate twice as fast, assuming mass remains constant.
Acceleration is inversely proportional to mass. If you double the weight, the object accelerates half as fast with the same force.
At higher speeds, I have proven that Force at the wheels decreases, due to gearing, air, and rolling resistance. As Force decreases, so must acceleration. Mass, however, remains a constant.
As Newton's equation shows, Mass actually has an increasing effect at higher speed where Force is decreasing. Reducing Force has the same effect as increasing Mass; acceleration decreases.
How about a few CarTest 2000 numbers where weight is the only change to back this up?
0-30 mph
2,800 lb. FD, stock engine - 1.93 sec.
3,300 lb. FD, stock engine - 2.15 sec. (+0.22 sec., +11%)
3,800 lb. FD, stock engine - 2.36 sec. (+0.43 sec., +22%)
100-130 mph
2,800 lb. FD, stock engine, 4th gear start - 10.31 sec.
3,300 lb. FD, stock engine, 4th gear start - 12.24 sec. (+1.93 sec., +18%)
3,800 lb. FD, stock engine, 4th gear start - 14.36 sec. (+4.05 sec., +39%)
If weight had less of an effect at high speed, you would expect the variance between the 100-130 acceleration times to be less than the 0-30 times, but it isn't. The variance is actually significantly higher. Obviously Mass has even more affect at higher speeds.
I know it seems like weight would have less of an effect at higher speed, once the chore of getting the car into motion is over, but that is not the case. That is simply something Supra owners tell themselves to feel better about having to have far more power to accelerate as quickly as an FD owner can with less. Their gearing and the fact that they can make more power is their only advantage.
Hey Jimlab do you deal with physics and all that other type science stuff alot. You always have these huge indepth equations backing these types of questions?
09-29-04, 12:18 PM
#27
Super Snuggles
Originally Posted by Ball joint
Hey Jimlab do you deal with physics and all that other type science stuff alot.
You always have these huge indepth equations backing these types of questions?
09-29-04, 12:19 PM
#28
Originally Posted by jimlab
. Obviously Mass has even more affect at higher speeds.
I know it seems like weight would have less of an effect at higher speed, once the chore of getting the car into motion is over, but that is not the case.
I know it seems like weight would have less of an effect at higher speed, once the chore of getting the car into motion is over, but that is not the case.
Solve your F=ma equation for a, you know a is smaller at higher speed due to the increase of all the forces the car is fighting. That means the F required to move the m is smaller at higher speeds (since a is smaller).
Where is Kevin K when you need him?
09-29-04, 12:42 PM
#29
Super Snuggles
Originally Posted by turbojeff
The car accelerates SLOWER at higher speeds due to all the drag, friction, rolling resistance, gearing, etc forces that are not present at 0 mph and don't get large until the velocity gets higher.
Solve your F=ma equation for a, you know a is smaller at higher speed due to the increase of all the forces the car is fighting. That means the F required to move the m is smaller at higher speeds (since a is smaller).
At 60 mph, you're only using about 10 horsepower to keep the mass of the vehicle in motion, give or take. Accelerating that mass from 60 mph to a given speed takes significantly more power, and the heavier the vehicle, the longer it will take. That is not debatable. Obviously mass does have a significant effect at higher speeds, until the losses from gearing reduction, drivetrain friction, air, and wind resistance exceed available power and the vehicle stops accelerating further.
If that's what you're referring to as mass being "less of a factor" at high speeds, then I'll concede that it could be viewed that way. The losses listed above do determine a vehicle's top speed. However, mass determines how long it takes to get there, or the rate of acceleration through the gears.
09-29-04, 01:14 PM
#30
Rotary Enthusiast
I'll try .... F = drive force at tire
CASE 1: ignore friction and drag
a=F/m
so for any gear and speed selected, added mass will proportionally decrease acceleration to the same degree.
CASE 2: consider a constant aero drag, which assumes a smallish speed change.
F-Fd=ma, a = (F-Fd)/m
again, acceleration will still be proprtional to mass, be it 2nd gear or 5th. For a wide speed change, integration of these small increments should come up with the same result ... acc'n proportional to mass.
CASE 3: consider only frictional drag (tires), proprtional to weight.
F-k(m) = ma, a =[F-k(m)]/m
here, the increase in mass also decreases the total driving force. and speed does matter ... mass hurts acc'n more at high speed.
ex: a 20% increase in m could stop acceleration in 5th where F is small to start with (100% change in acc'n), while in a lower gear acceleration still occurs, like a 30% change in acc'n.
CONCLUSION:
added mass will decrease acc'n more at higher speed, in the upper gears. This considers rear wheel torque, aero drag, and frictional losses related to weight.
CASE 1: ignore friction and drag
a=F/m
so for any gear and speed selected, added mass will proportionally decrease acceleration to the same degree.
CASE 2: consider a constant aero drag, which assumes a smallish speed change.
F-Fd=ma, a = (F-Fd)/m
again, acceleration will still be proprtional to mass, be it 2nd gear or 5th. For a wide speed change, integration of these small increments should come up with the same result ... acc'n proportional to mass.
CASE 3: consider only frictional drag (tires), proprtional to weight.
F-k(m) = ma, a =[F-k(m)]/m
here, the increase in mass also decreases the total driving force. and speed does matter ... mass hurts acc'n more at high speed.
ex: a 20% increase in m could stop acceleration in 5th where F is small to start with (100% change in acc'n), while in a lower gear acceleration still occurs, like a 30% change in acc'n.
CONCLUSION:
added mass will decrease acc'n more at higher speed, in the upper gears. This considers rear wheel torque, aero drag, and frictional losses related to weight.
Last edited by KevinK2; 09-29-04 at 01:18 PM.
09-29-04, 01:19 PM
#31
OK, so bottom line:
Increased weight is less of a factor in acceleration at higher speeds than it is at lower speeds.
Since CarTest is making assumptions we don't know, specially on the launch about I'd like to see what the test results are using the same example you did earlier but instead of starting the car at 0-30 mph start it with some initial velocity.
Also since your 100-130mph run probably included a shift and the 0-30mph run didn't it would be better to do a 2nd gear run from say 4000-7500rpm and then a 4th gear run in the same rpm range and compare the two.
That will better illustrate the point I believe.
Increased weight is less of a factor in acceleration at higher speeds than it is at lower speeds.
Since CarTest is making assumptions we don't know, specially on the launch about I'd like to see what the test results are using the same example you did earlier but instead of starting the car at 0-30 mph start it with some initial velocity.
Also since your 100-130mph run probably included a shift and the 0-30mph run didn't it would be better to do a 2nd gear run from say 4000-7500rpm and then a 4th gear run in the same rpm range and compare the two.
That will better illustrate the point I believe.
09-29-04, 01:54 PM
#32
Rotary Enthusiast
Originally Posted by turbojeff
OK, so bottom line:
Increased weight is less of a factor in acceleration at higher speeds than it is at lower speeds....
Increased weight is less of a factor in acceleration at higher speeds than it is at lower speeds....
09-29-04, 02:03 PM
#33
Super Snuggles
Originally Posted by turbojeff
OK, so bottom line:
Increased weight is less of a factor in acceleration at higher speeds than it is at lower speeds.
Increased weight is less of a factor in acceleration at higher speeds than it is at lower speeds.
Since CarTest is making assumptions we don't know, specially on the launch about I'd like to see what the test results are using the same example you did earlier but instead of starting the car at 0-30 mph start it with some initial velocity.
Also since your 100-130mph run probably included a shift
and the 0-30mph run didn't it would be better to do a 2nd gear run from say 4000-7500rpm and then a 4th gear run in the same rpm range and compare the two. That will better illustrate the point I believe.
Originally Posted by KevinK2
CONCLUSION:
added mass will decrease acc'n more at higher speed, in the upper gears. This considers rear wheel torque, aero drag, and frictional losses related to weight.
added mass will decrease acc'n more at higher speed, in the upper gears. This considers rear wheel torque, aero drag, and frictional losses related to weight.
09-29-04, 03:43 PM
#34
hmmm, well maybe I'm all wet but I don't think so. Consider acceleration at the limit.
At the limit, terminal velocity, wind drag rules the entire show, there is no acceleration. We all know this.
Right before we hit that limit acceleration is almost zero. That means any additional mass is accelerating very, very slowly. Referring back to F=ma, a is almost 0, effectively reducing the effect of any additional mass, at low speeds a is very high, maximizing the force required to accelerate additional mass.
At the limit, terminal velocity, wind drag rules the entire show, there is no acceleration. We all know this.
Right before we hit that limit acceleration is almost zero. That means any additional mass is accelerating very, very slowly. Referring back to F=ma, a is almost 0, effectively reducing the effect of any additional mass, at low speeds a is very high, maximizing the force required to accelerate additional mass.
09-29-04, 03:55 PM
#35
Rotary Enthusiast
Jeff, check my 1st post. case 2 shows that the mass effect is independent of the aero drag effect, doesn't matter if is high or low acc'n. see the case 2 formula ... I might have missed something .... don't think so
09-29-04, 07:00 PM
#37
Rotary Enthusiast
Originally Posted by the_glass_man
So basically if you got a fat *** friend riding with you and you might get in a show down on the highway kick his fat @$$ out! 
Although you lost less G's at 125, vs in the low gears, the % drop was higher at 125. Mabe that was the confusion point, you do lose more G's in the lower gears, but the % change in acceleration is less.
09-29-04, 10:34 PM
#38
Super Snuggles
Just for laughs, I ran a few more simulations with a stock FD changing only the weight. The extra weight steadily decreases acceleration as speed increases, even near top speed.
30-60 mph, rolling start, 2nd gear start
2800 lbs. - 3.26 sec.
3300 lbs. - 3.75 sec. (+0.49 sec., +15.0%)
3800 lbs. - 4.26 sec. (+1.00 sec., +30.7%)
60-90 mph, rolling start, 3rd gear start
2800 lbs. - 5.21 sec.
3300 lbs. - 6.05 sec. (+0.84 sec., +16.1%)
3800 lbs. - 6.91 sec. (+1.70 sec., +32.6%)
90-120 mph, rolling start, 4th gear start
2800 lbs. - 8.72 sec.
3300 lbs. - 10.27 sec. (+1.55 sec., +17.8%)
3800 lbs. - 11.92 sec. (+3.20 sec., +36.7%)
120-150 mph, rolling start, 4th gear start
2800 lbs. - 20.37 sec.
3300 lbs. - 25.01 sec. (+4.64 sec., +22.8%)
3800 lbs. - 30.84 sec. (+10.47 sec., +51.4%)
150-165 mph, rolling start, 5th gear start
2800 lbs. - 23.75 sec.
3300 lbs. - 34.92 sec. (+11.17 sec., +47.0%)
3800 lbs. - 63.83 sec. (+40.08 sec., +168.8%)
For the next sample, launch rpm was optimized for each weight prior to running the simulation.
Quarter Mile
2800 lbs. - 14.08 sec. @ 99.98 mph
3300 lbs. - 14.67 sec. @ 98.28 mph (+0.59 sec., +4.2%)
3800 lbs. - 15.25 sec. @ 94.58 mph (+1.18 sec., +8.4%)
30-60 mph, rolling start, 2nd gear start
2800 lbs. - 3.26 sec.
3300 lbs. - 3.75 sec. (+0.49 sec., +15.0%)
3800 lbs. - 4.26 sec. (+1.00 sec., +30.7%)
60-90 mph, rolling start, 3rd gear start
2800 lbs. - 5.21 sec.
3300 lbs. - 6.05 sec. (+0.84 sec., +16.1%)
3800 lbs. - 6.91 sec. (+1.70 sec., +32.6%)
90-120 mph, rolling start, 4th gear start
2800 lbs. - 8.72 sec.
3300 lbs. - 10.27 sec. (+1.55 sec., +17.8%)
3800 lbs. - 11.92 sec. (+3.20 sec., +36.7%)
120-150 mph, rolling start, 4th gear start
2800 lbs. - 20.37 sec.
3300 lbs. - 25.01 sec. (+4.64 sec., +22.8%)
3800 lbs. - 30.84 sec. (+10.47 sec., +51.4%)
150-165 mph, rolling start, 5th gear start
2800 lbs. - 23.75 sec.
3300 lbs. - 34.92 sec. (+11.17 sec., +47.0%)
3800 lbs. - 63.83 sec. (+40.08 sec., +168.8%)
For the next sample, launch rpm was optimized for each weight prior to running the simulation.
Quarter Mile
2800 lbs. - 14.08 sec. @ 99.98 mph
3300 lbs. - 14.67 sec. @ 98.28 mph (+0.59 sec., +4.2%)
3800 lbs. - 15.25 sec. @ 94.58 mph (+1.18 sec., +8.4%)
09-30-04, 11:52 AM
#39
I don't wanna mess w/ all the in-depth physics equations and what not, because that wasn't my strong point in college....but
This I gotta agree w/. I skimmed over the thread, and it seems that Jim's point wasn't clearly defined/understood. Whether weight is more or less of a factor at various speeds, I don't know. But the fact remains, speed IS very much A factor at higher speeds. In fact, to expand on Jim's comment, acceleration is defined as a change in velocity over time, correct? A = V/T, and we know that Force = mass * acceleration. Rearrange, A = Force/Mass. That relationship shows us that the greater the mass, the less the acceleration, irregardless of if you're starting from a dig, or you're doing a 100mph roll. The law still holds true.
Going back to the velocity part, your velocity is changing due to a force applied in a given direction. That force is invariably linked to the mass you are trying to move. The greater the mass, the greater the force necessary.
Yet, there's one more important variable at higher speeds...air resistance. And in fact, if I'm not mistaken, at speeds above 140mph, air resistance increases exponentially, while the force equation remains linear. The result? SINCE you're dealing w/ a much *much* greater resistance, it takes an increasingly greater force to accelerate the car any more...and w/o a doubt, the less the mass, the (relatively) greater force you have available for acceleration. So point being, a lighter car will definitely accelerate faster at higher speeds than the same car w/ the same hp but added weight. The heavier car will reach it's terminal velocity sooner, since the greater mass will have a larger impact on the same available force, thus capping acceleration at a sooner point... Does that make any sense?
Originally Posted by jimlab
I don't think you're getting it. Weight is still very much a factor at higher speeds. It doesn't matter where you start accelerating from, weight is still going to affect how quickly you accelerate up to the point at which losses exceed the available power.
Going back to the velocity part, your velocity is changing due to a force applied in a given direction. That force is invariably linked to the mass you are trying to move. The greater the mass, the greater the force necessary.
Yet, there's one more important variable at higher speeds...air resistance. And in fact, if I'm not mistaken, at speeds above 140mph, air resistance increases exponentially, while the force equation remains linear. The result? SINCE you're dealing w/ a much *much* greater resistance, it takes an increasingly greater force to accelerate the car any more...and w/o a doubt, the less the mass, the (relatively) greater force you have available for acceleration. So point being, a lighter car will definitely accelerate faster at higher speeds than the same car w/ the same hp but added weight. The heavier car will reach it's terminal velocity sooner, since the greater mass will have a larger impact on the same available force, thus capping acceleration at a sooner point... Does that make any sense?
Last edited by FDNewbie; 09-30-04 at 12:12 PM.
09-30-04, 12:37 PM
#40
Super Snuggles
Originally Posted by FDNewbie
The heavier car will reach it's terminal velocity sooner, since the greater mass will have a larger impact on the same available force, thus capping acceleration at a sooner point... Does that make any sense?
I was actually surprised to find that CarTest 2000 indicated different top speeds for each of the examples above. Because it greatly affected the results of calculating acceleration time from 150 mph to top speed, I used 165 mph as the cut-off for each car to make the simulation identical for each.
Obviously, I already knew that top speed is the point at which losses (drivetrain friction, rolling resistance, air resistance, etc.) exceed available power. What I didn't factor in was that the added weight increases rolling resistance or friction with the road surface, decreasing top speed.
09-30-04, 05:22 PM
#41
Rotary Enthusiast
jim, from Cartest output could you list the component forces for aero drag, total friction, and engine derived force for say 120 mph at 2800 lbs, and how 500 extra lbs changed the friction force?
09-30-04, 08:47 PM
#44
Super Snuggles
Originally Posted by KevinK2
jim, from Cartest output could you list the component forces for aero drag, total friction, and engine derived force for say 120 mph at 2800 lbs, and how 500 extra lbs changed the friction force?
2800 lbs.
3300 lbs.
3800 lbs.
Last edited by jimlab; 09-30-04 at 08:53 PM.
09-30-04, 09:39 PM
#45
Originally Posted by jimlab
The change is attributable to increased tire friction.
10-01-04, 01:42 AM
#46
2/4 wheel cornering fiend
Originally Posted by FDNewbie
I'm going to leave this as more of "just a thought" than a question, as I fear it may take us off topic...but that's very interesting, because if you do your job right, and take into account all the varying forces you're encountering (like Jim has), there is definitely a critical value you will find and must keep in mind regarding weight vs. speed, to ensure you have enough traction for pure safety's sake, right? Sure, the added weight may require greater hp to reach a given speed, but I'd think the alternative would be very poor traction (too little tire friction), the results of which would be devastating...
10-01-04, 02:21 AM
#47
Originally Posted by Kento
It's not so much for "pure safety's sake" as it is available traction to overcome the aerodynamic drag to even achieve those higher speeds. All things being equal (since there's so much theoretical figure-slinging going on here), you'll never even get to those speeds if you don't have the traction to begin with.
10-01-04, 08:39 AM
#48
Lives on the Forum
To essentially say what Kento said already you need enough load on the tire in order to hold enough traction to overcome aero drag and still have grip available to accelerate the car. You could have an engine with 10,000 horsepower but if you get to 180 mph and start spinning the tires (easier than you think if you have the power, especially when you consider most LSR runs are on packed sand or salt) you're not going to go any faster. That's why at really high speeds (150+) what really counts is aero factors. Horsepower is easy; you can always make more. The hard part is making the car stable and the tires still work at those speeds without inducing a lot of aero drag. You can easily do this by just making the car heavier; you may be suprised that many land speed record vehicles are actually quite heavy. They could create downforce aerodynamically but this increases drag and reduces engine power available for acceleration, there's no free lunch. Keep in mind though that LSR cars are built purely for top speed, they don't exactly accelerate quickly.
Most of the unlimited type LSR cars shoot for a slight amount of aero downforce and then keep plenty of weight for tire grip and so the car doesn't fly. Thrust SSC broke the sound barrier on land and it is not wheel driven but thrust driven. This means they don't need grip from the tire other than direction control as the engines provide pure thrust propulsion. That car weighed 8500 pounds! They started lighter but found they needed the weight even though this car had active aero aids and didn't rely on tire driven acceleration.
Most of the unlimited type LSR cars shoot for a slight amount of aero downforce and then keep plenty of weight for tire grip and so the car doesn't fly. Thrust SSC broke the sound barrier on land and it is not wheel driven but thrust driven. This means they don't need grip from the tire other than direction control as the engines provide pure thrust propulsion. That car weighed 8500 pounds! They started lighter but found they needed the weight even though this car had active aero aids and didn't rely on tire driven acceleration.
10-01-04, 11:54 AM
#49
2/4 wheel cornering fiend
You'd be surprised how much tire spin occurs without any aerodynamic downforce at high triple-digit speeds on pavement. I've seen reams of data acquisition logs from professional racing motorcycle teams that show the rear wheel speed exceeding the front wheel speed by as much as 4 mph in many cases. Bikes can't have the same aerodynamic downforce designed into their bodywork like automobiles because of their unique cornering dynamics, and they're so much "dirtier" aerodynamically that they struggle against aero drag to a much greater degree.