Graphs of wheel torque vs. speed for various gears...

[Dingleweed]

So, I have been doing a little homework trying to figure out if I want to get 4.10s or 4.30s. One thing that I did to help me decide was to graph the actual torque to the wheels (dyno WTQ x gear ratio x diff. gear ratio). For the dyno WTQ numbers I used this graph that I found for a stock 1999 Cobra:

(I forget where I found this, but it seems kind of typical, and my car is sort of near stock... for now... ;-) )

I then mapped out the torque curve and input the data into a data processing program that I use and calculated the torque to the wheels (after gears, and differential ratios). For speed I used the info for the stock 245/45R17 tires.

Here's the chart for 3.90 differential gears:

and for 4.10 gears...

and for 4.30 gears...

and for 4.56 gears...

Since actual torque to the wheels is directly proportional to your acceleration, just think of the vertical axis as the kick in the pants that you feel for that gear at that particular speed.

These graphs and data are rather useful for other things; for instance, thrust (forward force) is your torque to the wheels divided my the radius of your back tire. Since the stock 245/45R17 tires are close to a foot in radius (12.84") you can approximately think of the vertical axes as the forward thrust of your car. Then divide that number by your car's weight and you have your forward thrust in g's. (Of course this is all assuming that you don't break traction...) Also, where you see the curves for a given set of gears cross is your optimal shift point for maximum acceleration and 1/4 mile times.

I had the "fun" of analyzing this data for my own info and gear decision, but I thought the info and graphs might be useful for the rest of the community.

Enjoy... :-D

 

[COBRABRAD]

Great data - thanks.

 

[ka3ak]

Good work! I wanted to this for a while myself, but being the lazy guy that I am, I never got around to it. Thanks man!

 

[RioRed4v]

thats pretty sweet..i've always wondering what the torque comparisions were compared to gear set to gear set.

nice work.

although, i'm curious about rough torque numbers, because you dont any numbers on the side of the graph, other than the RPM's.

 

[RioRed4v]

also just noticed this comment

Also, where you see the curves for a given set of gears cross is your optimal shift point for maximum acceleration and 1/4 mile times.

so according that graph, its saying that the optimal 1-2 shift is roughly 3k rpm's?? :shrug:

either i'm reading the whole thing wrong, or that info is inaccurate. i really dont see shifting at 3k rpm's being the optimal shift point.

 

[Dingleweed]

also just noticed this comment



so according that graph, its saying that the optimal 1-2 shift is roughly 3k rpm's?? :shrug:

either i'm reading the whole thing wrong, or that info is inaccurate. i really dont see shifting at 3k rpm's being the optimal shift point.

They are color coded. So, If you are shifting from 1 to 2 with any "upper" diff. gear that you choose, you look for the next curve of the same color; i.e., if you have stock gears you are shifting from a red "1" to the red "2". If you have 4.30 gears, look at the 4.30 graph and shift from the blue "1" to the blue "2".

 

[RioRed4v]

hmm..still not making sense to me, because if i follow blue line to blue line, it would be roughly 2400 rpms (going off the 4.30 graph) for the 1-2. and for the 2-3 it would be roughly 1600 rpms and the 3-4 would be roughly 1400 rpms.

( *edit* or it speed related, and not rpm related?? )

definitely aint trying to put down your hard work, just trying to understand it better.


also, is there anyway to tell rough tq #'s ?? because on the side of the graph it says ft lbs, but its in incriments of 500 like it would be for RPM's.

 

[Dingleweed]

because on the side of the graph it says ft lbs, but its in incriments of 500 like it would be for RPM's.

You are correct. The vertical axis is in ft-lbs. But that is in ft-lbs of torque to the wheels and not rpms. Since the stock wheel/tire combo is close to a foot in radius, just think of the vertical axis as the "forward" force of the engine on the car. So, in first gear (with stock diff. gears) the forward force is close to the weight of the car, or roughly around 3000 to 3300 lbs. So, that would equate to a "rough" g of forward acceleration.

Let me know if that makes sense, and I will gladly try to explain it another way. :rockon:

 

[RioRed4v]

i think i'm understanding it a bit better. so its not really a sheet of estimated torque numbers that a dyno would read?? i was at first thinking it was a program that showed what gears would equal out to if they were to produce actual torque numbers.

 

[Dingleweed]

if i follow blue line to blue line, it would be roughly 2400 rpms (going off the 4.30 graph) for the 1-2.

For the 4.30 graph, at the top of first gear (6700 rpm) the torque to the wheels is 2724 ft-lbs and the torque in second gear at the same vehicle speed would be 2350 ft-lbs. So, shifting at redline would make sense.

 

[Dingleweed]

i think i'm understanding it a bit better. so its not really a sheet of estimated torque numbers that a dyno would read?? i was at first thinking it was a program that showed what gears would equal out to if they were to produce actual torque numbers.

Right, it is more of a graph that shows just how hard the back wheels can twist (and in what gear), for a given vehicle speed.

Twisting power of the rear tires is directly proportional to your acceleration... your "kick in the pants" feeling ;-)

 

[Dingleweed]

It is a little confusing because dyno graphs automatically calculate for gear ratios and differential ratios in order to "back track" to the torque the engine produces as a function of rpm. But in reality, the actual torque applied to the back tires is dependent upon the torque the motor makes multiplied by the gear ratios.

 

[RioRed4v]

For the 4.30 graph, at the top of first gear (6700 rpm) the torque to the wheels is 2724 ft-lbs and the torque in second gear at the same vehicle speed would be 2350 ft-lbs. So, shifting at redline would make sense.

where are you getting the rpm's from?

last question, i swear. its either been a longer day at work than i think, or i'm just retarded :bash:

 

[Dingleweed]

where are you getting the rpm's from?

last question, i swear. its either been a longer day at work than i think, or i'm just retarded :bash:

The only rpms are from the original dyno plot. I use the torque vs. rpm data of that plot to calculate actual wheel torque and speed for the subsequent plots. (I printed out the dyno plot I had and drew a grid on it to get the torque vs. rpm data.) Then from the torque vs. rpm data I calculated the rest.

last question, i swear.

Hey, bring them on.. :beer: I am not content until my data is understood. ;-)

 

[hatsharpener]

A plot that would have made more sense to everybody would be to plot them on the same x-axis where the x-axis is the engine RPM. Good plot though, I was goign to put up a toy plot later this evening myself.

 

[Dingleweed]

A plot that would have made more sense to everybody would be to plot them on the same x-axis where the x-axis is the engine RPM. Good plot though, I was goign to put up a toy plot later this evening myself.

Ask, and ye shall receive...

3.90 gears vs. 3.27 gears' torque to the wheels vs. rpm

4.10 gears vs. 3.27 gears' torque to the wheels vs. rpm

4.30 gears vs. 3.27 gears' torque to the wheels vs. rpm

4.56 gears vs. 3.27 gears' torque to the wheels vs. rpm

 

[stangbuff]

Glen,

I’ve also been thinking about changing gears but my concern has been one not often discussed. I don't fear the gear but don't want to be a slave to one either. Those of us more interested in cruising than racing don't want to have to shift all the time (not that shifting is a bad thing mind you). I'm looking for a happy balance between not enough gear (3.27's) and maybe too much gear. Thanks for the information, it allows me to extrapolate where 3.55's and 3.73's will be and is giving me some perspective and ideas.

 

[Dingleweed]

Glen,

I’ve also been thinking about changing gears but my concern has been one not often discussed. I don't fear the gear but don't want to be a slave to one either. Those of us more interested in cruising than racing don't want to have to shift all the time (not that shifting is a bad thing mind you). I'm looking for a happy balance between not enough gear (3.27's) and maybe too much gear. Thanks for the information, it allows me to extrapolate where 3.55's and 3.73's will be and is giving me some perspective and ideas.

To give you an idea of where I am coming from, my last project car was a 2003 Hyundai Tburon GT (around 3100 lbs). Stock WHP was around 135 and stock WTQ was around 140 WTQ. I got it up to 197 WTQ and 197 WHP naturally aspirated. Then up to 280 WHP and 254 WTQ supercharged, plowing the way into unknown territory... Another story... but what I am getting at is that I had 254WTQ with a 4.41 differential gear and a close ratio 6 speed tranny.

When I got my cobra with "more" WHP and more "WTQ" it felt... well sluggish. I want it to pull (WTQ per lb) just like my last car did... :burnout:
And my Cobra is esstentially stock... :beer: :rolling:

 

[RioRed4v]

so i'm assuming the lower lines are the higher gears. (i.e it starts off with 1, then next line down is 2nd, and so and so?)

if so, much easier for me to comprehend.

 

[Dingleweed]

so i'm assuming the lower lines are the higher gears. (i.e it starts off with 1, then next line down is 2nd, and so and so?)

if so, much easier for me to comprehend.

All of the red lines are the stock 3.27 gears. On each graph, the blue lines are the "higher", or more aggressive, differential gear compared to the stock 3.27 gears.

I can also make some plots of any differential gear ratio versus any other differential gear ratio versus speed or torque to the wheels. Whatever you want.

My brother has a 2002 Mustang GT with: rai, 75mm TB, upper plenum, pluenum spacer, prochamber, catback (and maybe some other stuff that I can't remember). He hasn't had his car dynoed, but is searching for a compatible dyno so that I can do the same with his info.