Thanks everyone.
The person who asked for proof has now accepted the statement (and also that a pilot doesn't need the proof) but it's raised my interest and it would be good to get to the bottom of it. Does anyone want to volunteer the maths? (I have A level maths and first degree level applied engineering maths but it seems a long time ago

)
HFD
who used to eat partial differentials, path integrals, grad, div, curl, poynting, stoke's, green's and assorted other delicacies for breakfast - but now prefers Alpen