Don M

Without it, you are lost in space nowdays.

As the years have past and we have mucho dyno, 1/4 mile times in terms of ET and 1/4 mile MPH data we are starting to get a handle on what is what in the HP department.

Many examples will follow and the formulas to how these numbers were calculated will as well. We can all use internet JAVA script stuff, but the raw math is the funnest part and a pencil and paper are easier to carry to the track.

Some history on the formulas and who developed them should be first. Circa 1986 Patrick Hale, a drag racer and engineer who curerntly resides in Arizona was the father of the formulas and several computer programs as well. Patrick is still in business and his work continues to this day in other engineering math formulas and codes for racers and engine builders. Computer version are for sale and work very well.

Firstly, these formuals are simple. Only a few variables are used. Horsepower, Weight of the vehicle, Terminal speed ( MPH ) and elapsed time ( ET ) With this data Patrick found he can very accurately give an answer. Typically less than 4% variance between what is measured and what is calculated.

ET: This involves the cube root of the weight to power ratio multiplied by the constant of 5.825. Patrick obtained the constants used by crunching the hard numbers from thousands if not tens of thousands of track times and known HP numbers.

So we need the weight in pounds the vehicle is and the known HP of the engine to get the estimate of the elapsed time it will take it to travel the 1/4 mile.

Lets get a 7000 lb truck down the 1/4 mile with 600 HP.

7000 lbs divided by 600 HP = 11.66. Now we need the cube root of 11.66. That is 2.267. Multiply that by the constant of 5.825 = 13.20 is the ET

Or here is the formula:

cube root of weight/HP x 5.825

Lets try 5580 lbs divided by 800 HP. That is 6.97. The cube root is 1.91. Multiplied by the constant of 5.825 we get 11.12 ET.

Both of these numbers we got are not what we have actually seen in testing so the formulas are not perfect for the Turbo Diesel engine VS the naturally aspirated engines used to obtain the constant in 1986. With all our track and dyno data we are convinced the constant should be lower. Closer to a 5.425 as a round number.

This gives us an ET of 10.36 and 12.29 for the 5580 and 7000 lb trucks respectively. This also reconciles the rear wheel HP VS the flywheel HP. As with all turbo engines, turbo size will change "your" constant. Spool up will effect the constant and the ET by some respect. In our case it was around 7%. Your results may vary.

MPH: The same data was collected up to 1986 by Patrick to obtain a MPH figure from the weight and HP. But this time we are dividing the HP by the weight of the vehicle and changing the constant to 234.

Example, the same 7000 lb truck that has the 600 HP would have a terminal velocity of 102.9 MPH using Patricks formula and constant of 234.

The cube root of 600/7000 is .44. Multiplied by the constant of 234 and you get a MPH of 102.9.

Lets try the 5580 lb truck.

Cube of 800/5580 is .523. Multiplied by the constant we get 122.3 MPH.

Both numbers again were not measured at this, but we know the Turbo Diesel has a power curve unlike a normally aspirated gas engine. We need to adjust the constant to better suit our needs. We typically use a constant of 250.

Now lets get the HP numbers from the known weight and the ET the vehicles ran at the track.

HP = the weight divided by the ET/5.825 cubed.

7000 divided by the 13.20 ET/5.825 cubed = 605 HP rough

But we have changed our formulas constant from Patricks 5.825 to our own 5.425 and the truck runs the 1/4 in 12.29, not 13.20

A note on changing constants: Measured HP from a calibrated instrument ( dynamometer ) and the track times of the vehicle you are working on can be used to change your constant. Do not automatically assume you can use our constant examples of 5.425 VS Patricks 5.825 and 250 VS the 234. Turbo sizes greatly effect the outcome. Altitude does as well, but too a small degree.


Lets play now with MPH and weight:

COMP461 ( Greg Hogue and Dr P ) have a drag truck that weighs a reported 2700 lbs and the terminal velocity is 154 MPH. We dont have any dyno numbers from him, but we have enough data to get them with or without his permission. LOL

HP = his MPH divided by the constant of 234 and cubed and then multiplied by his weight.

154/234 cubed x 2700 = 769 HP

That is using Patricks constant.

With my constant of 250 I get 630 HP at the rear wheels.

Now lets try his ET of 8.72 and weight to get the mysterious HP number and see where we are compared to his MPH HP calculation.

HP = the weight divided by the ET/5.825 cubed

2700/ 8.72/5.825 cubed or:

2700 divided by 3.3541 = 804 HP.

Very close to the 769 HP we calculated by his MPH earlier.

Now lets use my constant of 5.425 we use most often.

2700 divided by 4.1523 = 650 HP.

Again, close to the 630 HP I got from his MPH earlier.

Within 3% anyway.

My numbers and Patricks numbers are somewhat different in that we are using a chassis Dyno to derive our constants and calculating this back to the ET, MPH and weight. So we are getting a rear wheel HP number VS an advertised number like some vendors and OEM's use.

Try these yourself at the strip. At events you can get a HP number from a Dynojet and almost always take that back to the ET or MPH potential. Again, turbocharger and spool up can change the ET and MPH enough to throw off the calculations some. Keep that in mind and have some fun.

It is a great polygraph and a good way to get a handle on the reality of HP your new engine modifications or upgrades make without a dynamometer.

Don~

Don M

If you dont have a scientific calculator, you can use a standard cheesy model to get the cube root of any number as follows:

Clear the standard calculator and get the number you want on the screen.

Example get a 6 on the screen.

Push follwing buttons:

Square root 1 time = 2.4494897
Multiplication once = 2.4494897
Square root two times = 1.2510333
Multiplication once = 3.0643931
Square root 4 times = 1.072498
Multiplication once = 3.2865554
Square root 8 times = 1.00465585
Multiplication once = 3.3018658
And finaly the Square root once more = 1.8171036

This will give you the cube root of the original number or
1.8171036 x 1.8171036 x 1.8171036 = 6

Don~

hotdram

Aighhh, my head is spinning. Did you know a TI scientific calculator can bounce pretty high off of a desk when launched hard enough at it.

Off to find my abacus
(Also, do I get a master's degree for reading those posts )

~Rob

Don M

Abacus. LOL

The history of numbers and speech is interesting.

RamWheelsBy4

Ok, I could not read that, seems math has not been fun for a while now. Especially after last years tax return, I used a lot of those formulas and they did not help.

I quit after the first example of a 7000lb truck with 600hp that showed a 13.2s 1/4.

That means that my 7300lb truck that ran a 13.2s 1/4 has more than 600hp. Ok I quit at that point with a smile .

AK RAM

What that really means is my 7,900lb truck that ran a 13.15 1/4 has a LOT more power than yours! ...and it is just a wimpy SO engine!



Enough trash talk'n. I didn't understand any of that either.

Rods

i cheated butt i got 770 for Comp

http://www.speedworldmotorplex.com/calc.htm

Mcmopar

It is interesting that way the TD constants change as opposed to the NA gasser.

RamWheelsBy4

Now don't go trying to bust my bubble , I picked up 75-80rwhp just reading the first couple of sentences . Heck I might have to read the whole thing, no tellin how much power I would have by the end.

Don M

The constant will change some. Patricks constant took into consideration the tire slip, the polar moment of inertia, frontal area, and the other variables.

Firstly, the 4 wheel drive trucks will just have less slip, bottom line. The dragsters and light weight trucks like COMP runs will have more. I cant tell you a good number for the constant because I have no in person experience with these myself. It is somewhere in between the 5.825 and the 5.425 I use.

I think a good idea would be to ge the weights and times, either in MPH or ET and figure out what the big boys have for rough HP.

Actually I have spent days calculating everyone I know of, but I do not have the real numbers for weight. Only the guesses and hearsay from the internet.

Lets start with the Scheid Dragster and the current time of 8.38. I dont know the actual weight so I will figure it at 2200, 2500, and finally 2700 pounds. If it is over 2500 I would be surprised and suggest they do the old racing trick of adding "lightness"

HP = weight divided by the ET/5.825 cubed.

Break it down as follows: Take the ET (8.38) and divide it by the constant (5.825)

8.38/5.825 = 1.4386

Now take the 1.4386 and cube it as follows:

1.4386 x 1.4386 x 1.4386 = 2.9772

The final step is to simply divide the weight by the cubed number you just got.

2200/2.9772 = 734 That is your peak HP number developed in the run. So a 2200 pound vehicle with a ET of 8.38 needs around 740 HP.

Remember the frontal area of the vehicle will play a part. Dragsters have little drag. LOL. When compared to a pick up truck with huge frontal area and tons of room under it for air to hang on.

Lets use 2500 pounds:

2500/2.9772 = 839 HP

And Finally 2700 pounds

2700/2.9772 = 906 HP.

These are peak numbers developed in the run. Average is less.

Don~

Don M

COMPS are the worse I have calculated for the modifications, but they were his old engine. Perhaps they will have more this next go round.

We have his ET of 8.72 and his internet reported weight of 2750. This will give us his HP like magic! LOL

8.72/5.825 = 1.4969

cube that = 1.4969 x 1.4969 x 1.4969 = 3.3541

Divide his weight of 2750 by the 3.3541 = 819 HP

Remember his engine is P pumped and uses enough Nitrous to fill a hot air ballon. LMAO

He does have more frontal area than a dragster and on the other hand less traction than the 4x4 trucks at launch. So, his numbers are not perfect. I guess they are within 5% of what he actually has.

Don~

Don M

I get 686 HP for yours. Of course you have more traction than Patricks formulas used, but you also have lots of frontal area ( think barn door ) to push through the wind.

Its probably in all fairness around 600 HP at the rear wheels!! Not bad for a SO truck at all.

Don~

Don M

Now the cumminsracing dragster of Scott Bentz:

The best ET was 7.97

I dont know the weight so I started with 1900, 2100 and 2300. I doubt it is over that.

7.97/5.825 = 1.3682

1.3682 x 1.3682 x 1.3682 = 2.5612

1900/2.5612 = 741 HP @ 1900 lbs

2100/2.5612 = 819 HP @ 2100 lbs

2300/2.5612 = 898 HP @ 2300 lbs

The biggest wall in the way is that all the racers are getting smart and have stopped publishing their real world weight and some dont even have a HP number to publish.

If we could get a scale at these events and weigh them, we could see who has the steak and spuds and who does not.

Don~

Don M

Keating Machine has their weight posted on their site. Take it for what its worth. In the past many racers were good at playing games with numbers to freak out their competition. I am not sayng they are, but the HP is the highest I have seen yet. Close to the Garmon truck of Morrison

He ran a 8.90 and says the truck weighs 3550.

8.90/5.825 = 1.5278

cubed = 3.5661

3550/3.5661 = 995 HP!

I would love to see it on a scale. He would do himself good if it weighs that by showing who has the HP!

Don~

Don M

Ok Now Darrens Garmon tuned truck.

The weight is a reported and believeable 5580.

The ET here is Texas was a 10.40

10.40/53825 = 1.7854

cubed = 5.6912

5580/5.6912 = 980 HP!

Some reduction in the constant is needed because he has a 4x4 and cheater slicks on all four corners. Tire slip is certainly less than the 2WD Keating truck.

Darrens truck never dynos near 1000 HP. Typically high 7's to 800. The constant needs some tweaking. If we use my constant of 5.425 it is closer to 800 HP, I believe.

Around 790 HP by the math. My constant is not valid and neither is Patricks, but Jeff and company have the data to make the constant changes they need to be inline with their DynoJet numbers. I am only guessing. In my testing and Dyno tweaks, our best DynoJet tunes were not he best track tunes. They were close though. I suspect the Garmons have figured the same thing out.

All the trucks and dragsters need some tweaks with the math, but it certainly shows us what is going on in the power department in a broad sense.

Don~