Where does the factor 1.3 for Vapp come from?

The approach speed Vapp is usually given as 1.3 * Vs0, or 1.3 times the stall speed in landing configuration.

Why 1.3? What created a consensus of 1.3 * Vs0 as the generally accepted textbook approach speed?

• I don't have time to pull proper research, but it's looking light it may just have been an arbitrary "130% of stall speed in the landing configuration", safety margin from 1941 Aviation Regs that got translated into 1.3 Vs0 in the next few years' editions and have stuck since. Commented Apr 20, 2019 at 4:33
• @ryan Mortensen thanks, very interesting! Commented Apr 20, 2019 at 13:44

1.3 Vso is not a universal rule even for the same plane. First is extra weight, which requires higher AOA for adequate lift at the same speed, or greater speed at the same AOA. Approach a little faster if heavy. Next is CG. If CG is near limits, a little extra speed will help aerodynamic trim as you slow down. Finally, there is weather. Gusting winds or wind gradient (head wind dropping as you near the ground) should make the pilot consider adding a few knots to approach speed as well.

The best policy is to do what is safe for your plane. A very slow plane that lands at 25 knots may be more like 1.5 or higher, especially on a windy day.

1.3 Vso is a fairly good approximation for a plane that stalls around 50 knots, approaching at 65 knots.

Another consideration in approach is safely banking in the pattern. Stall speed increases with bank angle as follows.

Load factor G = 1/(cos bank angle) Stall Speed (Accelerated) = Vs x Square Root G

For 30 degree bank: G = 1/.8662 = 1.155 (thought I had it here for a second!)
Accelerated stall speed = Vs x 1.07

For 45 degree bank: G = 1/.7071 = 1.414 Accelerated stall speed = Vs x 1.18

For 60 degree bank: G = 1/.5000 = 2.000 Accelerated stall speed = Vs x 1.414

So we avoid steep turns in landing patterns as well! Yet another reason to add safety margin to approach speed.

• You aren't wrong, but you did not answer his question. Since, clearly, every situation is different as you've pointed out. Why is 1.3 the textbook number? Commented Apr 19, 2019 at 19:50
• Where do we get 1.3 is the OP's question. Commented Apr 19, 2019 at 22:34
• The "textbook" answer of either Vref or (1.3*Vs0) if Vref isn't published is found in the AIM. 5-4-7 first and second sentence regarding approach category of aircraft. Commented Apr 19, 2019 at 22:40
• Ok, I'll go with that and a NOTAM for people who approach slower than trainers such as the Cessna 172. See math in my edit, and thanks for getting me to dig a little more. Commented Apr 19, 2019 at 22:44
• Even that portion of the AIM does not explain -- Why 1.3? I would give my own answer, but I haven't because I don't know the answer to the specific, why?, question asked. Otherwise, I would be giving an opinion-based guess without documentation, which isn't appropriate for this format. Commented Apr 19, 2019 at 22:49