# HP / Optimum Shifting Point Calculator By Bowling

Proper placement of shifting points is a required for best ET and MPH. Drivers usually shift when a pre-determined RPM is reached, but often employ guess in determining what this value should be, or else brings the engine close to red-line (not always a happy event). There are two schools of thought (probably more) on on determining optimum shifting rpms: one is to find a shift RPM which brings you back to the same point on the horsepower curve (ie. horsepower is the same before and after shift, "straddling" the curve), and shifting so that one maintains the maximum area under the horsepower curve. The following computes both parameters, after entering the transmission gear ratios and the horsepower/RPM pairs.

Algorithm: The horsepower curve is handled as a piecewise cubic spline. The program will not interpolate beyond the user-entered RPM range, so the computed optimum must lie within the RPM range of horsepower, and the RPMs must be entered in ascending order, or bad thing may happen. Method 1 (maintaining the same horsepower value before and after the shift) uses a modified Newton search, and the the second method (maximum area under horsepower curve) uses a numerical minimizer (or maximizer of area-under-the-curve, in this case). Since the RPM after the shift depends on the "ratios" of the gear ratios, the difference between the RPMs before and after the shift grows with increasing RPMs. This makes the area under the curve method favor higher shift RPMs compared to the first method. Which one is better? You find out......

# Transmission gear ratios in descending order (leave unused boxes blank):

Transmission Ratio 1 (Low):

Transmission Ratio 2:

Transmission Ratio 3:

Transmission Ratio 4:

Transmission Ratio 5:

# Measured Horsepower and Associated RPM:

Enter Horsepower - RPM here, an ascending RPM order. Enter up to 9 pairs - leave unused inputs blank

Horsepower: RPM:

Horsepower: RPM:

Horsepower: RPM:

Horsepower: RPM:

Horsepower: RPM:

Horsepower: RPM:

Horsepower: RPM:

Horsepower: RPM:

Horsepower: RPM:

Press this button to submit a computation:

To reset the form input:

Bruce Bowling