What is the constant in this formula for additional lift?
The formula you have given looks strange to me, I have never seen it before. But possibly I can help you with the following brief explanation about kinematic relationships when flying under wind conditions.

Flight path velocity (VK) is the vector sum of aerodynamic velocity (VA) plus wind velocity (VW), see sketch. - When flying in a headwind condition aerodynamic velocity will increase and a pilot will need to decrease Alpha to keep the lift constant. It is the opposite way around in a tail wind condition. Now a pilot will have to increase Alpha in order to keep the lift constant and additionally will have to pay attention not to come too close to Alpha max. Or increase thrust.

If one uses the sketched kinematic relationships properly one does not need an additional formula for analysis.