Quarter Mile Calculator and 0–60 Simulator

The force model follows Beckman's The Physics of Racing, Part 9 (attached pp.33–37), with torque-curve interpolation, finite shifts and an explicit traction limit added. Gearing uses the same angular-speed relation as the tire calculator:

RPM is converted explicitly to/from rad/s. A five-knot linear torque curve holds its first endpoint below the lowest knot. First gear holds at least the specified launch RPM, representing an ideal slipping clutch; after lockup RPM follows road speed. The final torque point is redline. Both engine plots include every entered torque knot. On each linear segment $T(n)=an+b$, power is proportional to $an^2+bn$; its maximum is checked at both knots and at the interior stationary point $n=-b/(2a)$ when $a<0$. Reported peak power is taken from these analytic candidates, independently of the plotting grid.

Road load is $R_v=\tfrac12\rho C_d A v^2+C_{rr}mg$. Unlike Beckman's tentative speed-proportional tire loss (p.36), this tool uses constant $C_{rr}mg$. No coefficient is fitted to a vehicle test.

Beckman's Parts 1–2 (attached pp.8–10) give load transfer and the Coulomb tire limit. With rear static fraction $f$, height/wheelbase $q=h/L$, and no axle lift, rear-drive limiting acceleration is $(\mu gf-R_v/m)/(1-\mu q)$; front drive is $(\mu g(1-f)-R_v/m)/(1+\mu q)$. Ideal AWD uses $\mu g-R_v/m$. The corresponding tractive-force bound is clipped to $[0,\mu mg]$. Delivered force is the lesser of engine force and that bound; acceleration follows $a=(F_{\mathrm{drive}}-R_v)/m$.

Velocity advances with the current acceleration; distance uses the average of the old and new velocities. Shortened steps land on upshift RPMs, completed shift interruptions and the finish. Drive force is zero during each shift; a shift must finish before another begins. Redline limits speed in the final gear. Runs end at 402.336 m or 60 s. Threshold times use interpolation of the first crossing. Before any plotting compaction, every full-resolution state is used to compute acceleration extrema, force-balance and traction residuals, RPM and motion bounds, and both axle normal-load minima. With signed acceleration, $N_f=mg(1-f)-mah/L$ and $N_r=mgf+mah/L$; deceleration during shifts can unload the rear axle. If either normal load becomes nonpositive, result cards are withheld with a corrective message. The compact plotting history preserves each channel's global extrema, the neighbors of acceleration extrema, both sides of shifts and rollout/60 mph/trap crossings, and a budgeted uniform sampling. Numeric summaries do not depend on that plotting selection. ET and 0–60 subtract the rollout crossing time. Per the NHRA glossary, trap speed is 20.1168 m divided by the time across the final 66 ft; it is not instantaneous finish speed.

Default step refinement from 0.02 s to 0.005 s changes ET by about 0.001 s and trap speed by 0.009 mph. OpenStax's constant-acceleration dragster example tests the complete integration; Beckman's worked values test gearing, drag and the 1 g limit. Independent-review regressions cover a narrow torque/acceleration peak and rear unloading during a shift; an analytic quadratic-segment case checks an interior power maximum.

Full throttle on straight, level pavement in still air. Test mass includes occupants and fuel. Torque and gear defaults are deliberately illustrative. Constant drivetrain efficiency and rolling resistance; no rotating inertia, downforce, slope, tire growth, boost lag, torque converter, clutch-energy calculation or wheelspin transients. The traction limit represents ideal throttle control at peak grip, not an uncontrolled burnout. AWD assumes ideal axle torque allocation. Load transfer is quasi-static and neglects aerodynamic pitch moments and suspension transients. A speed limiter holds redline when sufficient drive force is available; no automatic downshifts are made. Reaction time is excluded, and rollout changes the clock rather than the physical finish location.

For preliminary comparisons of fixed-ratio road-car drivetrains and teaching. Five torque knots must be strictly increasing in RPM; active ratios must decrease; shift points must lie between launch RPM and redline. The simplified transfer equations require μh/L < 0.8 and strictly positive front and rear axle normal loads at every integration state, including shift deceleration. Either axle-lift condition, failed launch or failure to finish in 60 s withholds results with a corrective message. If 60 mph is not reached before the quarter-mile finish, its result is deliberately blank and a note explains why. Very low gearing can give a redline-limited pass. Real ET depends strongly on launch technique, actual dyno torque, tire condition, rotating inertia, atmosphere and shift behavior. Displayed hundredths are numerical resolution, not an accuracy guarantee. The OpenStax and 1 g cases are ideal mathematical limits, not validations of Top Fuel performance.