inertia-reduction for improving acceleration, a detailed analysis
07-21-2011, 11:18 PM
#1
Registered Member
Thread Starter
inertia-reduction for improving acceleration, a detailed analysis
Hi all
I just want to post up my recent findings on reducing inertia in order to improve acceleration.
First, a little bit about myself - I am reasonably competent in the field of kinetics and dynamics, as I am currently a PhD student in mechanical/controls engineering, and hold a masters degree in the same field. I drive a 2008 G37S Coupe 6MT, but not very often (I baby it)
Right now, my confirmed modding goals are: 1. Eibach springs, 2. GTM TT (some time down the road). My other modding 'guidelines' are a) dont mess with engine internals, and b) keep the luxury equipment c) make car accelerate faster d) handling upgrades are not a priority because I don't drive aggressively around corners
Recently I became obsessed with figuring out how to reduce inertia on my car so that it would accelerate faster. I didn't want to strip the car, because a) you need to remove a lot of non-rotational mass to get any meaningful performance increase, and b) I want to keep luxury equipment (and rear seats). So then I considered lightened rotational components.
After extensive research, I found lightened aftermarket parts for the flywheel/clutch assy, crank pulley, brake rotors, and wheels/rims/tires. While reducing the mass of ANY part of your car will improve acceleration, what most people don't mention is HOW MUCH improvement (and more importantly, the cost-effectiveness) we can get with each lightened part.
Since most of the information out there is anecdotal, I wanted to find out and prove the answers for myself (by deriving dynamic equations).
Attached is a zip file of an excel spread sheet that I made. You can select OEM or Mod parts from the red boxes to see what kind of acceleration improvements it would get you.
The first model is very simplified - it basically models how fast the engine can make one wheel spin, if the car was sitting on jack stands. It also assumes friction-less and inertia-less transmission-shaft-LSD-axel components (I don't have any info on those so I left it out). Even though unrealistic, the relative contributions to accel improvement is apparent. Most importantly, due to the different gear ratios, components at the crank and at the rotor will have different contributions to acceleration. Flywheel and wheels are best, rotors and pulley does basically nothing.
The second model is more realistic and incorporates the translational acceleration of the entire car. The derivations are energy-based, and is similar to the info from . It basically says the same thing as the first model, except that the acceleration gains are not as high (clutch assy and wheels can net you ~7% improvement in acceleration, under ideal/optimistic conditions. So this is an upper-bound %)
The third model is a simplified F=ma translational acceleration. It basically confirms that removing mass from the right rotational components will yield more gains than removing the same amount of mass from non-rotational components.
Conclusions:
to make car accelerate faster, in order of effectiveness:
1. more power/torque (i.e. TT)
2. reduce rotational inertia
Do my conclusions agree with what you guys experienced?
Anyway, some of you guys probably already knew all that, but I thought it would be nice to have some quantitative proof. My spreadsheet might also be helpful to others who are considering similar upgrades. Comments and suggestions are welcome.
P.S. I dont really like to talk in terms of HP gains because I think most of the time this is a misleading measure. It is a measure of power, or rate of work done, and is not an intuitive thing to understand, at least to me (someone once said HP is a number that help sell cars). I prefer equations of motions, where the input (torque, force) causes motion (angular, translational acceleration) to happen.
I just want to post up my recent findings on reducing inertia in order to improve acceleration.
First, a little bit about myself - I am reasonably competent in the field of kinetics and dynamics, as I am currently a PhD student in mechanical/controls engineering, and hold a masters degree in the same field. I drive a 2008 G37S Coupe 6MT, but not very often (I baby it)
Right now, my confirmed modding goals are: 1. Eibach springs, 2. GTM TT (some time down the road). My other modding 'guidelines' are a) dont mess with engine internals, and b) keep the luxury equipment c) make car accelerate faster d) handling upgrades are not a priority because I don't drive aggressively around corners
Recently I became obsessed with figuring out how to reduce inertia on my car so that it would accelerate faster. I didn't want to strip the car, because a) you need to remove a lot of non-rotational mass to get any meaningful performance increase, and b) I want to keep luxury equipment (and rear seats). So then I considered lightened rotational components.
After extensive research, I found lightened aftermarket parts for the flywheel/clutch assy, crank pulley, brake rotors, and wheels/rims/tires. While reducing the mass of ANY part of your car will improve acceleration, what most people don't mention is HOW MUCH improvement (and more importantly, the cost-effectiveness) we can get with each lightened part.
Since most of the information out there is anecdotal, I wanted to find out and prove the answers for myself (by deriving dynamic equations).
Attached is a zip file of an excel spread sheet that I made. You can select OEM or Mod parts from the red boxes to see what kind of acceleration improvements it would get you.
The first model is very simplified - it basically models how fast the engine can make one wheel spin, if the car was sitting on jack stands. It also assumes friction-less and inertia-less transmission-shaft-LSD-axel components (I don't have any info on those so I left it out). Even though unrealistic, the relative contributions to accel improvement is apparent. Most importantly, due to the different gear ratios, components at the crank and at the rotor will have different contributions to acceleration. Flywheel and wheels are best, rotors and pulley does basically nothing.
The second model is more realistic and incorporates the translational acceleration of the entire car. The derivations are energy-based, and is similar to the info from . It basically says the same thing as the first model, except that the acceleration gains are not as high (clutch assy and wheels can net you ~7% improvement in acceleration, under ideal/optimistic conditions. So this is an upper-bound %)
The third model is a simplified F=ma translational acceleration. It basically confirms that removing mass from the right rotational components will yield more gains than removing the same amount of mass from non-rotational components.
Conclusions:
to make car accelerate faster, in order of effectiveness:
1. more power/torque (i.e. TT)
2. reduce rotational inertia
a. lighter flywheel/clutch assy (+3.9% acceleration, upper-bound)
b. lighter/smaller wheels and tires (+3.5% acceleration, upper-bound)
Lighter crank pulley gets you almost nothing (and may get you some problems... something about lack of harmonic damper); neither do lighter brake rotors: should only upgrade rotors/brakes for increased braking performance.b. lighter/smaller wheels and tires (+3.5% acceleration, upper-bound)
Do my conclusions agree with what you guys experienced?
Anyway, some of you guys probably already knew all that, but I thought it would be nice to have some quantitative proof. My spreadsheet might also be helpful to others who are considering similar upgrades. Comments and suggestions are welcome.
P.S. I dont really like to talk in terms of HP gains because I think most of the time this is a misleading measure. It is a measure of power, or rate of work done, and is not an intuitive thing to understand, at least to me (someone once said HP is a number that help sell cars). I prefer equations of motions, where the input (torque, force) causes motion (angular, translational acceleration) to happen.
Last edited by harbin9er; 09-03-2011 at 10:36 AM.
07-24-2011, 02:43 PM
#2
Registered Member
Thread Starter
updated sheet
updated the original spreadsheet with an improved version:
1. removed the simple models; only the advanced model remains
2. tidied up some derivations and formulas to make it easier to read
3. added some energy calculations - going to lighter wheels and clutches can potentially decrease the amount of kinetic energy in the car by up to 8% (that means 8% less fuel needs to be burned). Lighter pulley and brake rotors have very little effect on energy.
so there you have it: if you want to make your car accelerate faster or be more fuel efficient, go for lighter clutches and wheels+tires. Pulleys and brake rotors don't have much effect.
1. removed the simple models; only the advanced model remains
2. tidied up some derivations and formulas to make it easier to read
3. added some energy calculations - going to lighter wheels and clutches can potentially decrease the amount of kinetic energy in the car by up to 8% (that means 8% less fuel needs to be burned). Lighter pulley and brake rotors have very little effect on energy.
so there you have it: if you want to make your car accelerate faster or be more fuel efficient, go for lighter clutches and wheels+tires. Pulleys and brake rotors don't have much effect.
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bos3ayd (10-15-2014)
08-25-2011, 07:32 PM
#6
Registered User
I think you deserve a medal, sir. Or maybe a Nobel Competition Prize lol. Anyway, great work. Most of my buddies drive mustangs and like to gloat about their 'muscles' lol. One of them drives a '10 Mustang GT. Although we haven't had an opportunity to compete, I do believe I've got him. Again, thanks for the work.
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08-25-2011, 09:32 PM
#8
Maybe you should also put into equation balance of the car. Ferrari F1 has more powerful engine vs Red Bull Renault. Yet better balance gives driver (Vettel & Webber) ability to maneuver course better.
Also under braking less mass on rotors equals faster deceleration. Which is main function of the braking system. Not to go faster.
Yes with lighter wheels have some torque gain. But lighter wheels give ability to remain in contact with the asphalt. Giving more traction, when you bump a pot hole For example. With heavier wheels, take more time up in the air not in contact with the ground. Vs lighter wheel will fall to the ground faster. Giving more traction. Also lighter wheels will contour matching small undulations on the asphalt better than heavier wheels. So there is more to less mass = faster acceleration.
Just because engine will accelerate faster, does not mean you will go faster. It is the hole package. No matter what you want to achieve. Aesthetics, acceleration, cornering abilities. Should put into account all the factors. For best balance, looks, and HP/TQ.
I have numerous customers who now runs TT on their G37. However just to drive them with added power, is horrible experience. You will have to feather the pedals so gently. For the wheels not to spin out of control. Also when you are cornering prior to TT you were able to do 45mph on 90 degree. With TT alone you will have to do 25mph or less. Because as soon as you put your foot down, your rear wheels will spin out of control. With added power you do need to balance the car for more braking. Better cornering, lighter wheels and grippier tires.
Also under braking less mass on rotors equals faster deceleration. Which is main function of the braking system. Not to go faster.
Yes with lighter wheels have some torque gain. But lighter wheels give ability to remain in contact with the asphalt. Giving more traction, when you bump a pot hole For example. With heavier wheels, take more time up in the air not in contact with the ground. Vs lighter wheel will fall to the ground faster. Giving more traction. Also lighter wheels will contour matching small undulations on the asphalt better than heavier wheels. So there is more to less mass = faster acceleration.
Just because engine will accelerate faster, does not mean you will go faster. It is the hole package. No matter what you want to achieve. Aesthetics, acceleration, cornering abilities. Should put into account all the factors. For best balance, looks, and HP/TQ.
I have numerous customers who now runs TT on their G37. However just to drive them with added power, is horrible experience. You will have to feather the pedals so gently. For the wheels not to spin out of control. Also when you are cornering prior to TT you were able to do 45mph on 90 degree. With TT alone you will have to do 25mph or less. Because as soon as you put your foot down, your rear wheels will spin out of control. With added power you do need to balance the car for more braking. Better cornering, lighter wheels and grippier tires.
09-03-2011, 11:08 AM
#10
Registered Member
Thread Starter
Maybe you should also put into equation balance of the car. Ferrari F1 has more powerful engine vs Red Bull Renault. Yet better balance gives driver (Vettel & Webber) ability to maneuver course better.
Also under braking less mass on rotors equals faster deceleration. Which is main function of the braking system. Not to go faster.
Yes with lighter wheels have some torque gain. But lighter wheels give ability to remain in contact with the asphalt. Giving more traction, when you bump a pot hole For example. With heavier wheels, take more time up in the air not in contact with the ground. Vs lighter wheel will fall to the ground faster. Giving more traction. Also lighter wheels will contour matching small undulations on the asphalt better than heavier wheels. So there is more to less mass = faster acceleration.
Just because engine will accelerate faster, does not mean you will go faster. It is the hole package. No matter what you want to achieve. Aesthetics, acceleration, cornering abilities. Should put into account all the factors. For best balance, looks, and HP/TQ.
I have numerous customers who now runs TT on their G37. However just to drive them with added power, is horrible experience. You will have to feather the pedals so gently. For the wheels not to spin out of control. Also when you are cornering prior to TT you were able to do 45mph on 90 degree. With TT alone you will have to do 25mph or less. Because as soon as you put your foot down, your rear wheels will spin out of control. With added power you do need to balance the car for more braking. Better cornering, lighter wheels and grippier tires.
Also under braking less mass on rotors equals faster deceleration. Which is main function of the braking system. Not to go faster.
Yes with lighter wheels have some torque gain. But lighter wheels give ability to remain in contact with the asphalt. Giving more traction, when you bump a pot hole For example. With heavier wheels, take more time up in the air not in contact with the ground. Vs lighter wheel will fall to the ground faster. Giving more traction. Also lighter wheels will contour matching small undulations on the asphalt better than heavier wheels. So there is more to less mass = faster acceleration.
Just because engine will accelerate faster, does not mean you will go faster. It is the hole package. No matter what you want to achieve. Aesthetics, acceleration, cornering abilities. Should put into account all the factors. For best balance, looks, and HP/TQ.
I have numerous customers who now runs TT on their G37. However just to drive them with added power, is horrible experience. You will have to feather the pedals so gently. For the wheels not to spin out of control. Also when you are cornering prior to TT you were able to do 45mph on 90 degree. With TT alone you will have to do 25mph or less. Because as soon as you put your foot down, your rear wheels will spin out of control. With added power you do need to balance the car for more braking. Better cornering, lighter wheels and grippier tires.
Lighter rotors under braking is a complex issue. I've only given it a bit of thought so far. If you brake and do not disengage the clutch, meaning the whole transmission is connected from the engine all the way to the wheels, then my calculations would be correct, and that a lighter rotor (because it has only a small contribution to the total rotational inertia) by itself would actually not significantly help the car decelerate faster. However, if you brake and disengage the clutch, that would be a different story. Lighter brake rotors would help more, probably. But like I said, lighter components from any part of the car is going to help improve the performance. The question is how much.
Another factor that may be considered is how lighter rotors can help you turn the wheel (and thus handling, maybe) better. When you steer, you are changing the direction of the angular momentum of the entire rotor/wheel assy, which requires exertion of torque. So, less rotational inertia = less torque required to change the direction of the angular momentum. I haven't given this much thought coz like i said, i dont really drive aggressively around corners
Basically, the whole aspect of suspension and car handling is beyond my scope of knowledge - it's very complex. However, I think that if one wants to upgrade the brake rotors, he should be doing it for improved braking performance (i.e. less brake fade, better cooling, etc), rather than for better accel/decel.I want to address what you said here: "Yes with lighter wheels have some torque gain". With all due respect, that is a misconception. The engine is still the same and outputting the same torque to the wheels, so the torque is still the same. What is happening is that lighter wheels allow it to accelerate faster, giving the illusion that there is more torque appearing at the wheels. Having said that, lighter components *generally* have less frictional loss, so it probably would get a bit more (but only minuscule) torque.
09-04-2011, 09:07 AM
#12
Registered User
Thanks for the great thread. I don't know how I missed it before. I have pondered similar thoughts wrt fuel economy/ acceleration.
Part of my obsession lays with the fact that I am averaging 19.7 mpg under normal driving. I don't want to change how I enjoy the car, so I just want to tweak the mpg to break the 20.0
This spreadsheet will help with the considerations and I didn't even have to break out my old textbooks!
Part of my obsession lays with the fact that I am averaging 19.7 mpg under normal driving. I don't want to change how I enjoy the car, so I just want to tweak the mpg to break the 20.0
This spreadsheet will help with the considerations and I didn't even have to break out my old textbooks!
12-19-2011, 06:04 PM
#13
Registered Member
Thread Starter
Thanks for the great thread. I don't know how I missed it before. I have pondered similar thoughts wrt fuel economy/ acceleration.
Part of my obsession lays with the fact that I am averaging 19.7 mpg under normal driving. I don't want to change how I enjoy the car, so I just want to tweak the mpg to break the 20.0
This spreadsheet will help with the considerations and I didn't even have to break out my old textbooks!
Part of my obsession lays with the fact that I am averaging 19.7 mpg under normal driving. I don't want to change how I enjoy the car, so I just want to tweak the mpg to break the 20.0
This spreadsheet will help with the considerations and I didn't even have to break out my old textbooks!
04-14-2012, 11:59 AM
#14
Registered User
Just popping back in. Have you updated the file for the Al or Carbon driveshafts?
I already run my sport tires at 2 psi over, so the tire pressure is not my issue...
I already run my sport tires at 2 psi over, so the tire pressure is not my issue...
04-28-2012, 06:01 PM
#15
Registered Member
Thread Starter
Hey, just did a quick eyeballed calculation for the Aluminum drive shafts that Z1 sells
To be honest I don't think it will help acceleration v much:
consider upgrading the clutch assembly:
IF (upgrading to lighter clutch) THEN
now consider upgrading the shaft:
IF (upgrading to lighter drive shaft) THEN
The shaft's rotational inertia is only 1/8th of the clutch assy, AND it would have less effect on the overall acceleration because it is further down the transmission (you need to take into account of gear ratios)
So I would say the lighter shaft would give much less than 0.5% improvement in acceleration.
But hey, like I said, lightening ANY component in your car is going to improve acceleration and fuel economy. The only question is whether it is cost effective to do so for such minor gains
To be honest I don't think it will help acceleration v much:
consider upgrading the clutch assembly:
IF (upgrading to lighter clutch) THEN
clutch rotational inertia decreases from 0.16 to 0.08 kg m^2
and
car accelerates up to 3.9% faster
End_IFand
car accelerates up to 3.9% faster
now consider upgrading the shaft:
IF (upgrading to lighter drive shaft) THEN
shaft rotational inertia decreases from 0.02 to 0.01 kg m^2
End_IFThe shaft's rotational inertia is only 1/8th of the clutch assy, AND it would have less effect on the overall acceleration because it is further down the transmission (you need to take into account of gear ratios)
So I would say the lighter shaft would give much less than 0.5% improvement in acceleration.
But hey, like I said, lightening ANY component in your car is going to improve acceleration and fuel economy. The only question is whether it is cost effective to do so for such minor gains
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warpeacelove (10-16-2014)