HP, Torque, Gears, Wheels, etc.

Richard Casto · **Posted:** Tue Dec 23, 2003 4:43 pm

Ok, I am doing some "what if" analysis on several car, engine, wheel package combos. I have some published dyno results (benchmark runs of stock cars on the same dyno), gear ratios and wheel diameters.

I am interested in doing some 2nd gear performance evaluations. I basically want to look at how these cars would perform on paper in 2nd gear (autocross purposes). But what I have not done before is convert HP to Torque, car speeds to RPM via the maze of overall wheel/tire diameter, final drive and gear ratios. I know the formulas are simple, etc. I just haven’t done this before.

An example of what I am looking to do is to look at both my current car which is a 98 Civic LX and a car like the 99-00 Civic Si. They have different gear ratios but the Si produces more power and torque but at a higher RPM. Should I be trying to convert engine/flywheel torque to torque at the wheels? I am assuming (hoping :oops:

) that with different gearing the Si will be able to apply more torque to the road (but with higher engine RPM) than my LX.

Also, is Torque/weight a ratio that I should look at or just HP/weight? As you would expect these cars don’t weight the same. :wink:

Can someone give me some tips and/or point me to some formulas?

Graham Jagger · **Joined:** Fri Aug 29, 2003 12:53 am **Posts:** 1718

RPM calculator:

For final drive ratio of 1.0
RPM = ((RE Ratio * MPH) / Tire Diameter) * 336

Calculate in each gear
RPM = (((RE Ratio * MPH) / Tire Diameter) * 336) * Trans Ratio

So get your Rear End (RE Ratio), MPH you are concerned about, Tire Diameter, 336 (magic number), and Transmission Ratio for each gear you're interested in. I only worried about 1st and 2nd gear for autox but I calculated for all gears so I could see where the top end was :lol:

Put it in a spreadsheet and then just poke in the numbers so you can experiment. That's how I did mine...

Graham

Kevin Hoff · **Posted:** Tue Dec 23, 2003 8:34 pm

I made one of these a few years back. It's got some fairly cool features and is a bit more precise than using the magic number 336, as all the equations are based on calculated figures. Here's a link:

http://bellsouthpwp.net/k/w/kwh29/image/gearchart.xls

LMK if it doesn't work for some reason. The G's equation is probably wrong. AFAIK everything else is correct.

--Kevin H.

Edit: the figures in there now are for my old Scirocco with some dreaming for the torque figures... :lol:

DickRasmussen · **Posted:** Tue Dec 23, 2003 9:12 pm

You can do some "ball park" approximations using your current car and its speedometer. Pick a reasonable speed range that involves one gear such as 30 to 50 or 60 and time the time it takes to get from one speed to the next. Start accelerating below the starting speed to minimize response time variables.

You can then do "what ifs" with the percentage changes that different gearing and tire sizes would cause. You can even do the same with power/torque increases. Assume that unless the engine is particularly peaky that the accel rate for a reasonable rpm/speed range will be relatively constant in second.

You can compare with road test data for the same speed ranges but watch out for shifts. When comparing road test data, sometimes it is better to use higher speeds/gears since shifts are minimized and minor timing errors become a smaller part of the total time. Not too fast though or wind resistance becomes an issue. You can see the effect of wind resistance by looking at the time between 10 mph increments.

Also note that road test data and "speeds in gears" can have significant errors even from Road and Track and Car and Driver. I ran into a major error in recent data on the 2003 Honda S2000 in a comparison test in C and D. Speeds in gears seemed much higher than they should be even though all the calculations checked out. It turns out they neglected to include the "reduction gear" in the S2000's trans so all their calculated speeds were about 16 percent too high!

I assume you know to be skeptical of most dyno numbers posted on the internet or in magazines.

Note that I have g-analyst data that shows my 114 HP FF accelerates at about 14.5 ft/sec/sec (.45 g) in its 66 mph second gear between about 35 and 65 mph. The car with driver weighs about 1120 lbs.

If you get really motivated you can solve for the acceleration time changes for different combinations. Then you can figure out how to solve for time to distance with different accel rates. This becomes more of an issue if your gearing choices include trying to run the shortest possible gear for most straights without running out of revs too soon (a second or so of rev limiter time once in a while can be your friend). See your friendly local physics book and go looking for a computer program to do the iterative math (hint: the HP Calculator SOLVE function will do the math).

Richard Casto · **Posted:** Wed Dec 24, 2003 1:07 pm

Thanks everyone for the info....

Kevin, I will play with that spread sheet.

I may convert it to use published tire diameter instead. I wonder if tire/tread width and aspect ratio is going to be accurate enough?

Dick, Yeah I know about the Dyno issue.

Right now I am looking at comparisions between four cars...

96-00 Civic LX 1.6L SOHC no-Vtec
96-00 Civic EX 1.6L SOHC Vtec
99-00 Civic Si 1.6L DOHC Vtec
02+ Civic Si 2.0L DOHC Vtec

I currently have the LX model. The EX and 02 Si are just for comparison purposes. The only car in this bunch that I might switch to is the 99-00 Si.

The dyno info I have comes from Comptech. They have published baseline info (actual values for every 200 RPM) for the those three cars. These dyno baselines are used to show improvements when using their headers and exhaust. I believe they are from the same dyno as well. The three 1.6L baseline values seem to track pretty well at low RPM (a few HP of each other) and that makes sense to me. The peak values also match well with specified HP when using a 13% drivetrain loss. It is on the upper end where things change and the EX and Si make more power at higher revs.

If will get really hairy if I start looking at dyno values for other cars and try to compare those to the Honda values I have.

DickRasmussen · **Posted:** Wed Dec 24, 2003 2:50 pm

Richard Casto wrote:

The dyno info I have comes from Comptech.

Good. If you can't trust Comptech, then I don't know who you can trust. FYI Doug Peterson and Comptech did the machine work on my Lotus Europa engine in about 1981/82 before they got real famous. Just a small shop. Doug was racing the Fortech Mini in SCCA at that time if I remember correctly. His dad was the architect that the company (UL) I used to work for used in California at the time. His father was very excited when Doug got invited to Japan by Honda. Comptech and Team Highball ended up being the two top teams in IMSA radial sedan racing. A lot of Team Highball and Dennis Shaw stuff is in my FF. Small world.

Graham Jagger · **Joined:** Fri Aug 29, 2003 12:53 am **Posts:** 1718

Richard Casto wrote:

I may convert it to use published tire diameter instead. I wonder if tire/tread width and aspect ratio is going to be accurate enough?

Richard. I used the published specs from each vendor for diameter. I also used the 336 number for calculations. For real world working numbers they are fine. In any gear at any given RPM my MPH is less than 2MPH off. Given the car is 12yrs old I'm sure there is some drivetrain slop and all involved. You will have to actually drive the car to verify them anyway.

Also another thing I encountered, especially in 1st gear. When I got into the range where I was pulling a lot of torque and then backed off the throttle I quickly received a torque induced oversteer for my efforts :lol:

So just remember there is also a backlash for keeping the tach wound up in low gears. Those formulas don't help for that. Just trial and error...

Graham

Richard Casto · **Posted:** Wed Dec 31, 2003 3:29 pm

Kevin Hoff wrote:

I made one of these a few years back. It's got some fairly cool features and is a bit more precise than using the magic number 336, as all the equations are based on calculated figures. Here's a link:

http://bellsouthpwp.net/k/w/kwh29/image/gearchart.xls

LMK if it doesn't work for some reason. The G's equation is probably wrong. AFAIK everything else is correct.

--Kevin H.

Edit: the figures in there now are for my old Scirocco with some dreaming for the torque figures... :lol:

Ok, since I have HP and not Torque values, I am changing the spreadsheet around. Kevin's uses Torque to calculate HP and I need to use HP to calculate Torque. No big deal on converting the formula. But when I looked at the formula in the spreadsheet, I was suprised to see that PI was involved. So I looked online to see what I could find regarding published formulas. Kevin's formula was....

HP = (Torque * RPM)/(PI * 3 * 550)

Using PI = 3.14159 this equates to....

HP = (Torque * RPM)/5184

Online I found many examples of this formula....

HP = (Torque * RPM)/5252

5184 != 5252

So I worked the 5252 number backwards to see if it was just using a less/more precise value for PI but it came back as 3.183 which is NOT the reason for the difference.

I then looked some more and found an equation to build the 5252 magic number....

5252 = 33000/(PI * 2)

Once again PI, but something different than Kevin used. But no explanation on where this 5252 formula comes from? The 33000 number from above when divided by 60 is 550 which is a magic number in Kevin's formula.

Ok, so which is the right one? Kevin's is so different than the other formula that I can't imagine it is a typo and the resulting 5252/5184 magic number values are so close to each other. :?:

DickRasmussen · **Posted:** Wed Dec 31, 2003 4:17 pm

Richard,

Where on the spreadsheet do you find the actual formulas? I'm not strong with Excel. All I found was what looked like references to the real formulas. i.e. $ signs in the cells.

In regard to PI, as I recall the normal HP to Torque formula doesn't need PI. This implies that since the spreadsheet is calculating acceleration of the car for various HP's or Torques that they are using the lever arm of the tire radius in their calculation. If they are working with tire diameter or revs per mile then there may be a "conversion" step that uses PI to get the radius.

Edit: I just looked at the spreadsheet. It starts with tire section width and aspect ratio and wheel diameter. Looks like it must be calculating the radius and/or the tires revs per mile somewhere (wish I could find the formulas) which probably is where PI is needed.

Somebody who remembers this stuff needs to chime in before I waste more time looking it up

Richard Casto · **Posted:** Wed Dec 31, 2003 5:46 pm

DickRasmussen wrote:

Richard,

Where on the spreadsheet do you find the actual formulas? I'm not strong with Excel. All I found was what looked like references to the real formulas. i.e. $ signs in the cells.

Example would be the HP calculation for 1000 RPM (Cell B5). The formula in the cell is...

=(C5*D25)/((PI()*3)*550)

C5 and D25 are variables that substitute the values for those cells. PI() is a formula that returns the value of "Pi". So in this case that would translate to..

=(Torque*RPM)/((PI*3)*550)

or

=(70*1000)/((3.14159*3)*550)

or

= 14 HP

DickRasmussen wrote:

In regard to PI, as I recall the normal HP to Torque formula doesn't need PI. This implies that since the spreadsheet is calculating acceleration of the car for various HP's or Torques that they are using the lever arm of the tire radius in their calculation. If they are working with tire diameter or revs per mile then there may be a "conversion" step that uses PI to get the radius.

Now that I think about it, it might be the Work/Power calculation is dealing with the rotational aspect (revs per minute) of how an engine does work vs. the simple linear work (i.e. ft) of Force * Distance.

DickRasmussen · **Posted:** Wed Dec 31, 2003 6:02 pm

Richard,

Thanks for showing me where PI shows up.

I guess the $ sign in many of the formulas has to do with absolute cell reference. Now all I have to do is figure out why that is necessary. Excel(lent) "learning opportunity"

Richard Casto · **Posted:** Wed Dec 31, 2003 6:15 pm

DickRasmussen wrote:

Richard,

Thanks for showing me where PI shows up.

I guess the $ sign in many of the formulas has to do with absolute cell reference. Now all I have to do is figure out why that is necessary. Excel(lent) "learning opportunity"

Going way OT here....

Sometime you may create a formula that you would like to use to "autofill" (or whatever Excel calls it) neighboring cells with. When you do this it will automatically increment the cell numbers (i.e. C4 may become C5, C6, etc.). That works well in this situation like this where you have formulas based upon RPM. But for some things you want to have the reference to not change when you do this. Another example would be the gear calcs. Regardless of the RPM you want to use the same final drive and gear ratio. So you use the "$" to lock down that part of the cell reference.

Happy New Years. :wink:

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