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Oct 8th, 2025
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  1. Short answer
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  3. Your implementation is not the canonical normalization used in the Pacejka combined formula.
  4. Because you compute G0 with the same Bxa that depends on k, the denominator shrinks when k (or RBX2) increases, so the ratio can increase — which is the behavior you observed.
  5. In the canonical / intended normalization the denominator is evaluated at a fixed reference value (effectively k = 0 baseline), so increasing k (or RBX2) makes the numerator move toward 1 while the denominator stays fixed — therefore Gx decreases (i.e. combined correction reduces longitudinal capability).
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  7. Why that happens (one-paragraph)
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  9. You have Bxa = (RBX1 + RBX3*yi*yi) * cos(atan(RBX2*k)). Larger RBX2*k → cos(atan(...)) falls → Bxa falls.
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  11. Both numerator and denominator in your Gx = Num(Bxa*As)/Den(Bxa*Shxa) depend on Bxa. Because As (ai+Shxa) is usually much larger than Shxa, the numerator changes faster toward cos(0)=1 than the denominator does. Thus the numerator/denominator ratio can grow, even though the underlying Bxa fell. That’s an implementation artifact from using the same B in numerator and denominator.
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  13. What Pacejka expects (practical canonical normalization)
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  15. The usual approach is to normalize by a baseline evaluated at the reference shift (so the denominator is effectively fixed). In practice you evaluate the denominator using the baseline B at k=0 (i.e. cos(atan(RBX2*0)) == 1), or explicitly evaluate at the reference slip shift Sh but using the baseline B (not current Bxa).
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