An earlier revision of this engine had a draft-equation error, and an earlier version of Tractor_Implement_Performance_Calculator.xlsx had three further formula errors — all found and fixed. The corrected spreadsheet has been re-checked cell-by-cell against this engine for its own default inputs — every intermediate value matches to 3–4 decimal places (Rr, Bn, μg, μ, TE, SFC, fuel, Put all confirmed exact). Details below for the record.
0. Draft force equation — confirmed against the primary ASAE D497.5 FEB2006 standard (most consequential fix).
The standard's own equation (§4.1.1) is D = Fi·[A + B(S) + C(S)²]·W·T, with T (tillage depth) in cm used directly — there is no division by 10 anywhere in the standard text. An earlier revision of this engine (and of the reference spreadsheet) divided depth by 10, understating draft force by exactly 10× for every major tillage tool. This has been corrected; draft, and therefore every downstream result (axle loads, traction, slip, power, fuel, ballast), is now roughly 10× larger than in earlier revisions of this tool for the same inputs — verified against the standard's Table 1 coefficients, which produce physically realistic draft figures (e.g. ~15.6 kN for a 1 m mouldboard plough at 20 cm) only without the /10.
1. Rear axle load (Rr) — operator-precedence error (fixed). The original formula divided only the last term (D·Yd) by the denominator (L−er+ef), instead of the whole numerator:
was: (Wi+Py)(...) + Wt(...) − (D·Yd)/(L−er+ef)
now: [(Wi+Py)(...) + Wt(...) − D·Yd] / (L−er+ef)
This had inflated Rr by roughly 2×, understating the wheel numeric Bn by ~40% and tractive efficiency by a similar margin.
2. Vertical soil reaction (Py) — wrong cell reference (fixed). Was Py = ratio × g (9.81); now correctly Py = ratio × D (draft force).
3. Hourly fuel consumption — wrong basis (fixed). Was Fuel = SFC × (rated PTO power × 0.88); now correctly Fuel = SFC × drawbar power (DBp), so fuel use responds to the actual operating condition again.
Measured effect of the original bug on wheel slip (3-bottom mouldboard plough, Captain DI 2600 tractor, CI = 1500 kPa) — kept here for reference:
| Depth / speed | Correct slip | Buggy slip | Error |
|---|
| 20 cm / 5 km/h | 2.80% | 2.40% | 0.40 pp |
| 25 cm / 6 km/h | 3.60% | 2.90% | 0.70 pp |
| 30 cm / 7 km/h | 4.70% | 3.60% | 1.10 pp |
The bug always made slip look lower and tractive efficiency look higher than reality — the dangerous direction for a decision-support tool.
Square-root guard. Every square root in this engine (wheel numeric in the traction terms, and the specific-fuel-consumption radicand) runs through a guard that raises a clear, named error — e.g. "Cannot compute wheel numeric (Bn) in traction term: square root of a negative value" — instead of silently producing NaN that would propagate through every downstream result.