For some time I have been looking for a simple stall speed equation that can factor in differing planetary conditions (gravity and air density) and changing vehicle mass, but have failed to find anything further than the standard stall speed equation:
v_stall = sqrt(2 * W/rho * S * C_L)
where,
v_stall = current stall speed
W = weight,
rho = air density,
S = wing area,
and C_L = max lift coefficient.
Additionally, I was looking for an equation that did not rely on wing area or lift coefficient. So, I derived my own expression. To be honest, I do not really remember how I came to it, I have been using it the past few years for hobby and conceptual design stuff, but it is the following:
v_stall = v_stall, 1g * sqrt( (1.225/rho_current) * (g_current/9.81) * (m_current/m_original) )
where,
v_stall = current stall speed
v_stall, 1g = stall speed under standard Earth conditions,
rho_ current = current air density,
g_current = current gravitational acceleration,
m_current = current vehicle mass,
m_original = original vehicle mass
It must be noted that v_stall, 1g is vehicle stall speed under 1 g and 1.225 kg/m^3 (standard Earth conditions)
This equation does work under theory and delivers results within a 1% to 3% difference from the standard equation. I ran calculations under many different air densities and gravitational accelerations, and the results almost always come startlingly close to the standard equation.
Can anyone else verify the validity of this equation?
Sorry for the poor formatting. I am new here.