I've noticed how often newbies (and not so newbies confused by the multi-voiced claims of the marketplace) seek help in determining which mod to start with, add on, or benefit from. Trying to find a logical method of quantifying in some way all these diverse mods is difficult, but I think I've come up with a method that will often work.
The August issue of MMFF features a column by Richard Holdener that contains some simple math one can use to compute the effect of a given modification on a given car. The logic goes:
1. Compute the number of g's (gravities) you car produced in current form. The example he used was a 5 speed car with 400 lb feet of torque, a 3.27:1 final drive and a 2.95:1 first gear ratio. Drivetrain efficiency was set at 87% (average for a 5 speed - automatics would be lower) to compensate for losses in the clutch, transmission and rear, and the tires had a rolling radius of 1.1 foot (racing slick, but close to that of many 315 drag radials as well). The car in the example weighed 3000 pounds. Here is the formula:
2.95 x 3.27 x 0.87 x 400 / (divided by) 1.1 = 3,356.98/1.1 = 3051.80 pounds of thrust. Next divide the thrust by the weight of the car:
3051.80 / 3000 = 1.017 g's of acceleration.
Changes to any of the variables will raise or lower the acceleration number, ie, add 100 lb/ft of torque with a nitrous kit, and you get 1.27 g's.
Change to 4.10 gears, and you get 1.278 g's.
Reduce the weight of the car by 600 lbs, and you get 1.271 g's.
Obviously you can also dollarize the equation, assigning the cost of the modification to the g's, ie:
Nitrous kit costs $1200, you gain .25 g's, the cost is $480 per .1 g gained.
Gears cost $600, you gain .25 g's, the cost is $240 per .1 g gained.
As you can see, the better investment purely from this standpoint are the Gears - more "bang for the buck".
The article contains many caveats regarding things like aerodynamic drag not being factored into the equation - and this is true. But this forumula is at least invaluable in prioritizing the various modifications in a quasi-scientific manner. Just plug in your particular variables, and you have a number that means something.
If you can find it, seek out the article and read it (he has a similar write-up in the July issue regarding lateral acceleration, ie, handling and braking, that has similar potential in determining which handling modifications to do first).
I think aerodynamic loads get discussed next month. I for one am all ears.
__________________
tripleblack
"You can never be free until you let yourself go."
I guess I will have to find the article and read it because I dont understand how you can divide thrust by weight and get anything else but a factor. Pounds divided by pounds cancel each other in an equation such as this. Acceleration or g's are expressed in ft x sec x sec....?
DSS 331 stroker, AFR 185 heads, Performer rpm 2 intake, Accufab 75 mm race TB, 30lb injectors, 80 mm Pro-M mass air, Extreme energy cam 266.
Anderson ford power pipe the big one, Ford motor sport shorty headers, Bassani x pipe custom cat back with flows, World class T5, center force duel friction clutch.
3.27 (final drive ratio) x 2.95 (gear ratio in first gear - formula will work with any gear, so if you want to use 2nd or 5th gear, go ahead)
recap:
[3.27 x 2.95 x 400 (torque in #')] divided by 1.1 (size of the tire) =
subtotaled:
3, 356.98 / 1.1 (divided by 1.1) = 3051.80 pounds of thrust (not pounds of weight)
then
3051.8 pounds of thrust / (divided by) 3000 pounds (weight of the car) = 1.017 G's of acceleration.
Tell you guys what, imagine you are considering adding a blower that will add 150 pounds to the weight of the car and add 150 foot pounds of torque...
3.27 x 2.95 x 550 = 4340.925 / 1.1 = 3946.30 / 3150 pounds = 1.253 G's of acceleration.
You gained .183 G's from the modification.
The same formula can be used to analyze the effects of different gear sets, different handling accessories (how much will those 20" wheels cost you because they add 100# to the weight of the car?), etc, etc, etc.
The NEXT step is to take your list of mods that you are considering, run the math on each one, and figure out which ones give you the most gain.
As you can see, its a fraction (.183 is actually a sizeable gain). If you list everything (gears, blower, ported heads, new cams, whatever) and take each fraction and multiply it by its $ cost, you can get a prioritized list that logically tells you which mods will give you the best cost/performance benefits!
I know, it seems mind boggling - but only at first. Work through the formula a few times, it will sink in. Especially when you realize that FOOT pounds of force and WEIGHT pounds are very different things. One is the moving force - and the other is the thing being moved.
Quote:
Originally Posted by tripleblack
1. Compute the number of g's (gravities) you car produced in current form. The example he used was a 5 speed car with 400 lb feet of torque, a 3.27:1 final drive and a 2.95:1 first gear ratio. Drivetrain efficiency was set at 87% (average for a 5 speed - automatics would be lower) to compensate for losses in the clutch, transmission and rear, and the tires had a rolling radius of 1.1 foot (racing slick, but close to that of many 315 drag radials as well). The car in the example weighed 3000 pounds. Here is the formula:
2.95 x 3.27 x 0.87 x 400 / (divided by) 1.1 = 3,356.98/1.1 = 3051.80 pounds of thrust. Next divide the thrust by the weight of the car:
3051.80 / 3000 = 1.017 g's of acceleration.
Changes to any of the variables will raise or lower the acceleration number, ie, add 100 lb/ft of torque with a nitrous kit, and you get 1.27 g's.
Change to 4.10 gears, and you get 1.278 g's.
Reduce the weight of the car by 600 lbs, and you get 1.271 g's.
Obviously you can also dollarize the equation, assigning the cost of the modification to the g's, ie:
Nitrous kit costs $1200, you gain .25 g's, the cost is $480 per .1 g gained.
Gears cost $600, you gain .25 g's, the cost is $240 per .1 g gained.
As you can see, the better investment purely from this standpoint are the Gears - more "bang for the buck".
The article contains many caveats regarding things like aerodynamic drag not being factored into the equation - and this is true. But this forumula is at least invaluable in prioritizing the various modifications in a quasi-scientific manner. Just plug in your particular variables, and you have a number that means something.
If you can find it, seek out the article and read it (he has a similar write-up in the July issue regarding lateral acceleration, ie, handling and braking, that has similar potential in determining which handling modifications to do first).
I think aerodynamic loads get discussed next month. I for one am all ears.
__________________
tripleblack
"You can never be free until you let yourself go."
I still contend the formula comes up short because for a "g" to be involved, there has to be a time factor. There is no time factor in the above formula. A "g" is defined as the acceleration of the same magnitude as the value of the acceleration due to gravity on Earth at sea level or 32 ft per second squared. How long will this 1.017 g's last? 1sec? 2sec? throughout the entire rpm range? Are "g's" directly proportional to ET's? At what throttle setting? Shut to open or half-shut to open?
Either something is missing in the formula or in my brain and I probably wont sleep tonight unitl I figure it out.......frymahide!
I still contend the formula comes up short because for a "g" to be involved, there has to be a time factor. There is no time factor in the above formula. A "g" is defined as the acceleration of the same magnitude as the value of the acceleration due to gravity on Earth at sea level or 32 ft per second squared. How long will this 1.017 g's last? 1sec? 2sec? throughout the entire rpm range? Are "g's" directly proportional to ET's? At what throttle setting? Shut to open or half-shut to open?
Either something is missing in the formula or in my brain and I probably wont sleep tonight unitl I figure it out.......frymahide!
Gs are the time factor -it's 9.8 meters per second. acceleration in gravitational units.
__________________
Woe to him who builds his palace by unrighteousness,his upper rooms by injustice,making his countrymen work for nothing...Does it make you a king to have more and more cedar?Did not your father have food and drink?He did what was right and just,so all went well with him. He defended the cause of the poor and needy,and so all went well...But your eyes and your heart are set only on dishonest gain,on shedding innocent blood and on oppression and extortion. Jer 22:13, 15-17
I still contend the formula comes up short because for a "g" to be involved, there has to be a time factor. There is no time factor in the above formula. A "g" is defined as the acceleration of the same magnitude as the value of the acceleration due to gravity on Earth at sea level or 32 ft per second squared. How long will this 1.017 g's last? 1sec? 2sec? throughout the entire rpm range? Are "g's" directly proportional to ET's? At what throttle setting? Shut to open or half-shut to open?
Either something is missing in the formula or in my brain and I probably wont sleep tonight unitl I figure it out.......frymahide!
Note the use of a "rolling radius". I think this is the variable you are looking for. Time is NOT being deduced here (except very indirectly - it could be, but then the math WOULD be tough - and the amount of time it takes the tire to go that distance is teeeeeeeny tiny). The idea is to approximate about an hour's time on a supercomputer, getting numbers with a meaningful basis (though not necessarily one that would enable us to put a man on Mars) without too much agony.
ET's could be inferred, but then you start getting into the variables of friction (surface, working (tire contact patch), and air), aerodynamic loads, etc ad nauseum.
Its NOT an engineering number to build to - its an approximate number which makes it possible to determine a PATH to plan the build. Its why I call it a "quazi-scientific" method. Its like using a slide-rule before calculators - they were approximate tools - but boy, they got you there a whole lot quicker than doing it with a pencil and 5000 sheets of paper.
Lord help us, I could probably dig up all the formulas for a tighter plan - but the equipment needed to measure things to arrive at remotely accurate results would cost a bloody fortune. "Data logging" doesn't begin to explain it.
Elapsed times are best left to real world results rather than modeling in the mathematical universe.
BUT trying to figure out which modification to do first, second, third, and what proportional change might it make to your results?
Sure. If the formula says you will gain 4% acceleration from a given mod, then you can expect that to translate into 4% less time on your et - ASSUMING an absolute TON of variables all fall right, of course (we won't even think about coming up with a mathematical method of predicting a human being's reaction time with any accuracy)!
__________________
tripleblack
"You can never be free until you let yourself go."
I'm still confused, but too simplify the math part since I only have 6th grade comprehension LOL, I compare proven methods first.
mod (1) gears
mod (2) under drive pulley.
mod (3) CAI, and K&N air filter
mod (4) tune up oil change, and ignition system with high output coil.
mod (5) custom tune, done.
Advanced guys.
mod (6) heads, cam, intake.
mod (7) custom built motor.
mod (8) power adder, supercharger, or turbo.
Don't forget to take fuel, and fuel management systems into consideration when passing the 300 HP level.
__________________
DSS 331 stroker, AFR 185 heads, Performer rpm 2 intake, Accufab 75 mm race TB, 30lb injectors, 80 mm Pro-M mass air, Extreme energy cam 266.
Anderson ford power pipe the big one, Ford motor sport shorty headers, Bassani x pipe custom cat back with flows, World class T5, center force duel friction clutch.
My problem is that it's limited to drag strip acceleration. It doesn't say much about say 55-85 mph acceleration. Only 0-XX acceleration.
I think that may be what artistang was getting at . .
__________________
Woe to him who builds his palace by unrighteousness,his upper rooms by injustice,making his countrymen work for nothing...Does it make you a king to have more and more cedar?Did not your father have food and drink?He did what was right and just,so all went well with him. He defended the cause of the poor and needy,and so all went well...But your eyes and your heart are set only on dishonest gain,on shedding innocent blood and on oppression and extortion. Jer 22:13, 15-17
My problem is that it's limited to drag strip acceleration. It doesn't say much about say 55-85 mph acceleration. Only 0-XX acceleration.
I think that may be what artistang was getting at . .
Plug in the gear you prefer.
2nd? 3rd?
It still works.
If you're referring to handling, absolutely, it can only give a partial picture (ie, how much any addiitonal weight or weight reduction affects the car). Holdener never came back with the promised article about handling math (that I ever saw - I'll have to do a search and see if he published it elsewhere).
But you can use it for a simple snapshot of performance in any gear. If you want to establish and ET, as I said earlier, that's NOT what its for, and to do that you need a math model composed of dozens (perhaps hundreds) of similar formulae being fed with some pretty serious measuring devices to establish and backup your findings.
Lockheed is nearby - I suppose they might loan me their wind tunnel and statistical analysis array...
Nah.
Anyway, it really does work to prioritize things and give you a general idea of what will affect the performance - if not a god-view of the future. Remember, I said its a means of winnowing down the endless array of potential mods to those that best meet your specific needs.
It can supplement empirical experimentation and actual results - but it won't completely replace them by any means.
__________________
tripleblack
"You can never be free until you let yourself go."
If you're referring to handling, absolutely, it can only give a partial picture (ie, how much any addiitonal weight or weight reduction affects the car). Holdener never came back with the promised article about handling math (that I ever saw - I'll have to do a search and see if he published it elsewhere).
But you can use it for a simple snapshot of performance in any gear. If you want to establish and ET, as I said earlier, that's NOT what its for, and to do that you need a math model composed of dozens (perhaps hundreds) of similar formulae being fed with some pretty serious measuring devices to establish and backup your findings.
Lockheed is nearby - I suppose they might loan me their wind tunnel and statistical analysis array...
Nah.
Anyway, it really does work to prioritize things and give you a general idea of what will affect the performance - if not a god-view of the future. Remember, I said its a means of winnowing down the endless array of potential mods to those that best meet your specific needs.
It can supplement empirical experimentation and actual results - but it won't completely replace them by any means.
of course! sorry, just looked at it while managing the cardomain thing.
The corvette, RX8, and S-10 are rattling me.
__________________
Woe to him who builds his palace by unrighteousness,his upper rooms by injustice,making his countrymen work for nothing...Does it make you a king to have more and more cedar?Did not your father have food and drink?He did what was right and just,so all went well with him. He defended the cause of the poor and needy,and so all went well...But your eyes and your heart are set only on dishonest gain,on shedding innocent blood and on oppression and extortion. Jer 22:13, 15-17
OK, plug in the variables. To work the math, you first need to know...
1. What is your final drive gear ratio right now?
2. What is your 1st gear ratio (or pick any other gear you like)?
3. What is the weight of your car?
4. What size tires are you using?
5. What type of transmission do you have (auto tranny's are less efficient than manuals)?
6. How much torque are you currently producing?
Once you determine these baseline numbers, you can plug them into the formula and arrive at your existing state.
THEN you start doing "what if" runs.
Change out the gears to 4.10's? 3.73's? 4.30's? (This is any easy one, since you only have to change out one number in the formula).
Underdrive pulleys? Here you need to know what your torque gain is, and you can either do before and after dyno runs (expensive) or go by what the manufacturer claims.
Any modification that changes any of the variables can be run through and compared to any other modification that does the same thing.
I've done this, and once you weight them by $$$, NOTHING beats gears. Unfortunately, even this process will only HELP you with your planning, not do it for you. For instance, a KB twin screw develops so much torque that they don't recommend strong gears - in fact, your 3.27's will work just fine with a strong KB install. The numbers in that case lie to you, because they DO NOT include a variable for traction (which is where wider knowledge and experimentation come in handy).
Its a helper, not a magik wand.
Quote:
Originally Posted by mustanghelper
I'm still confused, but too simplify the math part since I only have 6th grade comprehension LOL, I compare proven methods first.
mod (1) gears
mod (2) under drive pulley.
mod (3) CAI, and K&N air filter
mod (4) tune up oil change, and ignition system with high output coil.
mod (5) custom tune, done.
Advanced guys.
mod (6) heads, cam, intake.
mod (7) custom built motor.
mod (8) power adder, supercharger, or turbo.
Don't forget to take fuel, and fuel management systems into consideration when passing the 300 HP level.
__________________
tripleblack
"You can never be free until you let yourself go."
OK, plug in the variables. To work the math, you first need to know...
1. What is your final drive gear ratio right now?
2. What is your 1st gear ratio (or pick any other gear you like)?
3. What is the weight of your car?
4. What size tires are you using?
5. What type of transmission do you have (auto tranny's are less efficient than manuals)?
6. How much torque are you currently producing?
Once you determine these baseline numbers, you can plug them into the formula and arrive at your existing state.
THEN you start doing "what if" runs.
Change out the gears to 4.10's? 3.73's? 4.30's? (This is any easy one, since you only have to change out one number in the formula).
Underdrive pulleys? Here you need to know what your torque gain is, and you can either do before and after dyno runs (expensive) or go by what the manufacturer claims.
Any modification that changes any of the variables can be run through and compared to any other modification that does the same thing.
I've done this, and once you weight them by $$$, NOTHING beats gears. Unfortunately, even this process will only HELP you with your planning, not do it for you. For instance, a KB twin screw develops so much torque that they don't recommend strong gears - in fact, your 3.27's will work just fine with a strong KB install. The numbers in that case lie to you, because they DO NOT include a variable for traction (which is where wider knowledge and experimentation come in handy).
Its a helper, not a magik wand.
Unless you choose (3rd) 4th, 5th or (6th) gear . ..
__________________
Woe to him who builds his palace by unrighteousness,his upper rooms by injustice,making his countrymen work for nothing...Does it make you a king to have more and more cedar?Did not your father have food and drink?He did what was right and just,so all went well with him. He defended the cause of the poor and needy,and so all went well...But your eyes and your heart are set only on dishonest gain,on shedding innocent blood and on oppression and extortion. Jer 22:13, 15-17
Modificaiton Math 
