I divided the 1/4 mile drag race into 3 parts, a) 0 to 30 MPH, where launch techniques including dumping the clutch, tire spin, etc..., help to apply as much HP to the ground as quickly as possible to get the truck rolling, b) 30 to 60 MPH, where shifting through 1st, 2nd, and 3rd gears keeps the RPM in the power band for getting the maximum HP applied to the ground, and c) 60 to 90+ MPH, where WOT is maintained in 4th gear the rest of the way to the finish line.

I ran one piece of the model at a time to see what each piece contributes to the overall results, and to double check all the equations and their interactions with each other. A summary table (pic #6) is given which shows that the whole is equal to the sum of the parts. I could use some inputs to see how well the model predicts actual results, and any ideas for making it better or more complete. I ran 5 cases, shown in pics #1 to #5, which I call...

(1) Ideal, No Drag, No Slipping, No Shifting, Constant 340 RWHP: This run doesn't include the effects of rolling resistance and aerodynamic drag. The maximum 340 RWHP is applied to the track continuously, and the tires have perfect traction so that all the force this HP generates is available to accelerate the truck. This run requires a continuously variable gear ratio so that the engine can operate at the RPM for maximum HP throughout the entire run, and tires that stick like glue and transfer all this HP to the ground. It also requires a good head rest restraint so that you don't break your neck during launch! This is the absolute best that can be done with 7200 lbs and 340 RWHP.

In pic #1, the blue curve is a flat line indicating that all the HP is continuously being applied to the ground, and that without drag it's all being used to accelerate the truck, and produce the %g acceleration given by the gold curve, which is read on the right scale where the maximum value is 150%g or an acceleration of 1.5 g which is 1.5*32.174=48.261 ft/sec2. The shape of the %g curve results from the force being generated between the tires and the ground which is F=(375*HP)/(MPH), and for a constant HP this force is large at low MPH, and then decreases to ever smaller values as the MPH increases.

The red ED curve is also read on the right scale, and indicates the 1320 ft mark at 101.6 MPH. To show the ET curves results in too much clutter on the graph, but all the results are shown in the summary box on each graph.

(2) Drag, No Slipping, No Shifting, Constant 340 RWHP: This run is identical to (1) except that the effects of rolling resistance and aerodynamic drag are included. The HP is still being continuously applied to the ground as indicated by the flat green line, but as the blue curve indicates, above about 30 MPH an ever increasing amount of this HP is needed to overcome rolling resistance and aerodynamic drag, and the exact amount is just the difference between the curves.

(3) RWHP Required For Aerodynamic Drag & Rolling Resistance: This run shows the RWHP required to compensate for rolling resistance and aerodynamic drag for several reference vehicles, and for an F350 at several ambient temps, and at a 6 K altitude like in Denver. The aerodynamic drag force is proportional to the drag area, Ad, and to the atmospheric pressure, AP, and inversely proportional to the absolute temp in Kelvin. The close together red, blue, and green curves show the sensitivity to temp for an F350, and the center blue curve for 80 F at an AP of 14.7 psi is the standard curve used in all my drag runs.

Going from sea level (14.7 psi) to 6 K altitude (12.2 psi) this blue curve moves all the way over to the lime one shown for F350 Denver. It's interesting to note that (12.2/14.7)*(31.22)=25.9 vs the 24.9 Ad for the Hummer H2, so that an F350 in Denver almost has a drag as low as for the Hummer H2 at sea level.

Towing my 5er on the flat at 65 MPH requires 104.1 HP, which is why my engine compartment gets hot after towing awhile with the A/C on, but compared to the 18 wheeler which requires 182.5 HP I guess I've got it easy, of course he's got more HP than me, and he needs it.

(4) No Drag, Slipping, Shifting, Variable RWHP 340 Max: This run doesn't include rolling resistance and aerodynamic drag, but does allow for tire slippage and shifting. A typical PSD HP vs RPM curve is used with a maximum 340 RWHP at 2850 RPM. The amount of HP applied to the ground at a given MPH depends on the engine RPM resulting from the overall gearing, which takes into account tranny gear ratios, shift points, diff ratio, and tire diameter. For launch, the TC is assumed to be near the stall RPM of about 2000 RPM.

Since there's no drag, the HP curve is in blue indicating that all the HP is being used to produce the acceleration given by the gold curve. The blue curve doesn't peak until after 25 MPH, so that during launch the acceleration isn't determined my the maximum HP, but by wheel spin and traction considerations. The RPM curve is in pink, and shows where each shift point occurs. I intentionally chose these shift points to maximize the HP over time for the HP vs RPM curve in the model.

(5) Actual, Drag, Slipping, Shifting, Variable RWHP 340 Max: This run includes all the parts together, and is intended to provide realistic results for the assumed weight, HP, drag coefficient, etc... The green and blue curves are almost identical up to 35 MPH, so drag has little effect on the 60-ft performance. Optimizing the shifting keeps the green curve as high as possible, but the blue curve that's producing the acceleration is falling due to increasing drag. At the 1/4 mile mark, the blue curve is only 51.5% of the green curve, and the %g is down to 0.099 g. I let the model run on out to the 115 MPH top speed, and at that point the gold curve is 0 so that no more acceleration is possible, and all the HP is being used to overcome drag.

The last pic #6 is a summary table that shows the individual pieces really do add up to the actual run to within a fraction. I'm pleased (and a little surprised) it worked out this close, because the model employs some nonlinear interpolation.

 

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Gene, what does your wife do during the days?