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Background: many wildfire models simulate fire spread by resolving the front-normal velocity (spread rate) as a function of the local environmental conditions and the orientation of the fire front. We study one such model, here called the wind-projected Rothermel model, which extends the Rothermel model to all front orientations by using the front-normal component of the midflame wind speed \( \vec{U} \): \( R(\vec{n}) = R_0 (1 + A \max(0, \vec{n} \cdot \vec{U})^B) \) Methods: we apply the mathematical methods recently developed by the authors to solve front propagation in spatially constant conditions. Results: as soon as wind is moderately high, the model undergoes heading fire collapse, i.e. the downwind-facing front collapses to a pointed shape, which then advances at a lower speed than predicted by the Rothermel model. Formulas are derived to compute the characteristic length and time scales of the collapse. The effect is more pronounced for finer fuels that have a higher wind exponent. Conclusions: the formulas provided here can facilitate model validation. Heading fire collapse is frequent in this model; this is a salient point for model validation, as it makes the model behavior drastically different from other Rothermel extensions, like those based on elliptical Huygens wavelets. This also threatens the validity of some numerical implementations.