Here's how to determine your RWHP at a given RPM by making a timed acceleration measurement from MPH1 to MPH2 followed by a timed "coasting in neutral" deceleration measurement from MPH2 to MPH1. I'll first outline the test and then give numerical examples for my Freightliner towing my trailer and for a typical F350.

This road test self calibrates for aerodynamic drag and rolling resistance and it's even more accurate if you're towing a trailer because the extra load lengthens the intervals for the timed acceleration and deceleration measurements and longer time intervals can be measured with a higher percentage accurately.

Applying a constant throttle setting to go a constant MPH on a flat road applies a constant RWHPd to overcome the truck's aerodynamic drag and rolling resistance. If you increase the throttle setting you increase the RWHP by an amount RWHPa which is available to accelerate the truck to a higher MPH. Your total RWHP is given by RWHP=RWHPa+RWHPd and this test determines these two components of your total RWHP at a particular RPM.

Step #1... Weigh your truck to get its weight W.

Step #2... Find a flat stretch of road and select a gear that puts your RPM at the value RPM* where you want to determine a single point RWHP* at RPM* on your overall RWHP vs RPM curve.

Step #3... Reduce your RPM by 100 RPM or so below RPM* to a value RPM1 where your speedometer reads MPH1. Increase your RPM by 100 RPM or so above RPM* to a value RPM2 where your speedometer reads MPH2.

Step #4... Reduce your speed well below MPH1 so that your RPM is about 500 RPM below RPM* and settle into a constant speed. Then apply WOT and start your stop watch as you pass through MPH1 and stop it as you pass through MPH2, and measure the time interval Ta required to accelerate from MPH1 to MPH2.

Step #5... Now you're going faster than MPH2 so shift into neutral and coast, and as you coast through MPH2 start your stop watch and then stop it as you coast through MPH1, and measure the time interval Td that aerodynamic drag and rolling resistance acted on your truck to decelerate it from MPH2 to MPH1.

Step #6... Plug the above data set into these equations.

RWHPa={(W)(MPH2^2-MPH1^2)}/{(Ta)(16,452.6)}

RWHPd={(W)(MPH2^2-MPH1^2)}/{(Td)(16,452.6)}

RWHP*=RWHPa+RWHPd

RPM*={(0.5)(RPM1+RPM2)}

MPH*={(0.5)(MPH1+MPH2)}

This gives your RWHP* at RPM* which is the average value of your RWHP between RPM1 and RPM2, and your RWHPd at MPH* which is the average value of your RWHPd between MPH1 and MPH2.

To get the best accuracy for these RWHP estimates repeat these measurements several times and do them while going in each direction on the same stretch of road to average out any changes in grade or wind condition.

Here's an example for my Freightliner towing my trailer in 4th gear where RPM*=2,200 determines the RWHP* at the RPM* for its maximum 300 FWHP. My data set is W=32,000 lb, MPH1=55 at RPM1=2,100, MPH2=60 at RPM2=2,300, Ta=7.5 sec, and Td=10.8 sec. Plugging these numbers into the equations gives...

RWHPa={(W)(MPH2^2-MPH1^2)}/{(Ta)(16,452.6)}={(32,000)(60^2-55^2)}/{(7.5)(16,452.6)}=149.1 HP

RWHPd={(W)(MPH2^2-MPH1^2)}/{(Td)(16,452.6)}={(32,000)(60^2-55^2)}/{(10.8)(16,452.6)}=103.6 HP

RWHP*=RWHPa+RWHPd=149.1+103.6=252.7 HP

RPM*={(0.5)(RPM1+RPM2)}={(0.5)(2,100+2,300)}=2,200 RPM

MPH*={(0.5)(MPH1+MPH2)}={(0.5)(55+60)}=57.5 MPH

So my RWHP is 252.7 HP at 2,200 RPM, and my RWHPd is 103.6 HP at 57.5 MPH.

Here's an example for a tuned F350 7.3L PSD 3.73 Diff 4R100 in 3rd gear where RPM*=2,800 determines the RWHP* at the RPM* for its maximum FWHP. The F350 data set is W=8,000 lb, MPH1=65 at RPM1=2,600, MPH2=75 at RPM2=3,000, Ta=3.0 sec, and Td=8.7 sec. Plugging these numbers into the equations gives...

RWHPa={(W)(MPH2^2-MPH1^2)}/{(Ta)(16,452.6)}={(8,000)(75^2-65^2)}/{(3.0)(16,452.6)}=226.9 HP

RWHPd={(W)(MPH2^2-MPH1^2)}/{(Td)(16,452.6)}={(8,000)(75^2-65^2)}/{(8.7)(16,452.6)}=78.2 HP

RWHP*=RWHPa+RWHPd=226.9+78.2=305.1 HP

RPM*={(0.5)(RPM1+RPM2)}={(0.5)(2,600+3,000)}=2,800 RPM

MPH*={(0.5)(MPH1+MPH2)}={(0.5)(75+65)}=70.0 MPH

So for a tuned F350 the RWHP is 305.1 HP at 2,800 RPM, and the RWHPd is 78.2 HP at 70.0 MPH.

In my next installment I'll explain why a dyno reading is a little lower than the RWHP given above, and how to estimate your FWHP.

 

it would be less confusing to just go to a dyno!

 

Awesome Write-up! I'm going to do it this weekend. Is there any harm in shifting an auto into neutral at 75 mph?

 

Or just SWAG it!

 

I talked with a guy the other day and he's like "I've got dat d'ere SuperChips 'cuz it be da best, and gots me some 4" exhaust and the highest flowing intake there be, so with what they give me I knowz Ima puttin' over 400 horses to da pavement.."

Who needs scientific testing? We've got advertising!

 

That's funny chit there!!! Haven't we all heard that before!

Great info Gene. I'll have to go back through it again, but might just give it a try.

 

I don't think coasting in neutral for 30 sec or so with the engine at idle RPM and the transmission output shaft turning at road wheel driven driveshaft rpm will be an issue because the transmission receives pressurized fluid for lubrication from the flywheel driven impeller in the TQ convertor. Towing companies even claim that it's safe to tow for a moderate distance with the drive wheels on the ground by leaving the engine running and the tranny in neutral! You could always rev the engine to 1,500 RPM or so while coasting in neutral for additional lubrication.

 

I just use a G-tech. Works good. Says I have 1000HP

 

Man, that's some good info there. Would you happen to have a copy in english? Or maybe southeast redneck? It has been way too long since I have had to use that part of my brain.

 

I've looked at the "G-Tech" web site and as far as I can tell they only talk about measuring your truck's acceleration and that's not enough data to determine the total RWHP that your truck's applying to the road. Perhaps the user guide that came with your G-Tech has additional details that aren't given on their web site?

The gravitational acceleration constant is g=32.174 ft/sec/sec and converting that to MPH gives g=21.937 MPH/sec. The acceleration is given by A={MPH2-MPH1}/{Ta} MPH/sec, and Ga={A}/{g} gives the "g#" that's displayed on your G-Tech screen. For example a Ga=0.8 reading on your G-Tech screen means an A={(0.8)(21.937)}=17.55 MPH/sec, and your truck's MPH will increase by 17.55 MPH for every sec you see a Ga=0.8 reading displayed.

Assume you had the truck I used in my example and you use your G-Tech to measure that truck's acceleration over the 65 to 75 MPH interval. That gives an A={MPH2-MPH1}/{Ta}={75-65}/{3.0}=3.333 MPH/sec or a Ga={A}/{g}={3.333}/{21.937}=0.152.

In general Fa=mA lb where Fa lb is the FORCE that's accelerating the truck's mass m={W}/{g} and this gives Fa={(W)(A)}/{g}={(W)(Ga)} lb. So for W=8,000 lb and Ga=0.152 you get Fa={(W)(Ga)}={(8,000)(0.152)}=1,216 lb.

In general a RWHP that's applied to the road generates a push FORCE that's given by FORCE={(RWHP)(375)}/{MPH} lb so that the RWHPa that accelerates a truck is given by RWHPa={(Fa)(MPH)}/{375} HP so you get RWHPa={(Fa)(MPH)}/{375}={(1,216)(70)}/{375}=226.9 HP which is the exact same answer my formula gave for the RWHPa component of the total RWHP at the 70 MPH* mid point corresponding to the 2,800 RPM* which is the RPM at which the maximum HP occurs.

Now if the G-Tech measures and displays a "negative Ga" reading when the truck is decelerating you could use your G-Tech to measure the deceleration Ga from 75 to 65 MPH and calculate the RWHPd component of the total RWHP at the 70 MPH* mid point and then get RWHP*=RWHPa+RWHPd which is the total RWHP at the 70 MPH* mid point.

Do you have any idea how the G-Tech measures or estimates the component of RWHP that's being used to overcome the truck's aerodynamic drag and rolling resistance?

The formulas I give in my road test procedure are much simpler than using acceleration to get the FORCE and then the FORCE to get the HP. The TIME rate at which a truck can increase its kinetic ENERGY determines its ability to accelerate from a lower MPH speed to a higher MPH speed, and a trucks kinetic ENERGY is given by KE={(W)(MPH^2)}/{29.9138} ft-lb.

The TIME rate at which a truck can increase its kinetic ENERGY is determined solely by its RWHP because RWHP is defined as the TIME rate of ENERGY production so that RWHP={ENERGY}/{(TIME)(550)} where ENERGY is in ft-lb and TIME is in sec.

This gives RWHPa={[(KE2)-(KE1)]/[(Ta)(550)]} when accelerating from MPH1 to MPH2 in a TIME Ta, and it gives RWHPd={[(KE2)-(KE1)]/[(Td)(550)]} when decelerating from MPH2 to MPH1 in a TIME Td. The only number that changes is the Ta and the Td because the change in KE is the same whether you go from MPH1 to MPH2 or go from MPH2 to MPH1!

 

Well,he sounds pretty convincing to me,so I guess since its all kinda confusing,we could all meet up somewhere and Gene can just plan on riding up and down the road with us all,work the numbers for us,and give us each our RWHP...LOL...

 

What is the constant, 16,452.6?

I don't see how it can be really accurate because the rolling resistance, slope of road and air resistance will differ on each test.

 

A trucks kinetic ENERGY is given by KE={(1/2)(m)(V^2)} where m is the mass of the truck which weighs W lb and V is the truck's velocity in ft/sec. In the English units I'm using m=(W/g) where g=32.174 ft/sec^2 is the gravitational acceleration constant so the units for KE={(1/2)(m)(V^2)}={(1/2)(W/g)(V^2)} are (lb)(sec^2/ft)(ft^2/sec^2)=ft-lb.

If you multiply the KE={(1/2)(W/g)(V^2)} equation by {(88)/(60)}^2 to convert from V in ft/sec to MPH and substitute g=32.174 ft/sec^2, you get KE={(W)(MPH^2)}/{29.9138} ft-lb. So at speed MPH1 you get KE1={(W)(MPH1^2)}/{29.9138} ft-lb and at speed MPH2 you get KE2={(W)(MPH2^2)}/{29.9138} ft-lb.

The RWHPa that's required to accelerate the truck to increase its speed from MPH1 to MPH2 in a TIME Ta which increases its kinetic ENERGY from KE1 to KE2 in a TIME Ta is given by RWHPa={KE2-KE1}/{(Ta)(550)}. If you substitute the KE1 and KE2 into this equation you get RWHPa={(W)(MPH2^2-MPH1^2)}/{(Ta)(29.9138)(550)}={(W)(MPH2^2-MPH1^2)}/{(Ta)(16,452.6)}!

So the 16,452.6 constant comes from multiplying the 550 constant in the HP equation HP={ENERGY}/{(TIME)(550)} by the 29.9138 constant that results from converting kinetic ENERGY KE={(1/2)(m)(V^2)} to English units KE={(W)(MPH^2)}/{29.9138} ft-lb. The 550 constant from the HP equation is due to the fact that 1 HP produces 550 ft-lb of ENERGY per sec.

The road needs to be flat, but other than that my procedure of accelerating from MPH1 to MPH2 in a TIME Ta to get RWHPa and then immediately decelerating in neutral from MPH2 to MPH1 in a TIME Td to get RWHPd self calibrates for aerodynamic drag and rolling resistance, and even for any head wind or tail wind as long as the wind is the same during the 60 sec or so it takes to do both the acceleration and the deceleration measurements.

The RWHPd that's determined by the deceleration measurement is the part of the total RWHP that was being used to overcome the aerodynamic drag and rolling resistance during the acceleration measurement so you could be towing a trailer or whatever and you'll still get an accurate total RWHP measurement!

If you make measurements running empty and on some other day when towing you'll be able to get the aerodynamic drag and rolling resistance for each configuration and tell how much extra drag the trailer is causing! You'll get the same total RWHP=RWHPa+RWHPd whether empty or towing, but the component RWHPd will be larger when towing and the RWHPa will be less.


I'm going to post some graphs with arrows pointing to key features and try to explain how it works that way so stay tuned!

 

Very interesting Gene, WOW... I,m printing this out for step by step...great writeup.

 

Just did this, at 3200rpm, it says RWHP=718, and RWHPd= 112 @80mph