Delta v inclination change

[yomahabaca]

Hello I noticed in ksp rss ro principia that when I make a 90 degree tilt change around the earth it takes me a delta v of 12100m / s as shown in this picture     

on the other hand when I calculate the delta v necessary for the maneuver it gives me  = 10 930 m / s

why are the results different?

 

Edited September 16, 2021 by yomahabaca

[antipro]

1 hour ago, yomahabaca said:

Hello I noticed in ksp rss ro principia that when I make a 90 degree tilt change around the earth it asks me for a delta v of 12100m/s as shown in this picture. (image)
on the other hand when I calculate the delta v necessary for the maneuver it gives me  = 10 930 m/s
why are the results different?

I don't know, I just translate.

Edited September 16, 2021 by antipro

[OHara]

The formula you used is correct for an instantaneous burn to go directly from the first velocity to the second.

Principia computes the burn assuming you rotate the craft as the prograde/normal/binormal coordinates rotate. Principia rotates the instantaneous velocity of the craft through part of a circle, and that requires more delta-V (in this case, π/2× rather than √2× the orbital velocity).

@jd284 figured this out recently in the Principia thread (despite some confused and incorrect arguments given there)

[yomahabaca]

What formula did you use to arrive at the second result of your image?

Edited September 17, 2021 by yomahabaca

[OHara]

The delta-v in the case where you rotate the velocity keeping constant speed, is just the length of that arc.

follow : Δv = 2 v sin(Δi/2)

follow : Δv = v Δi   (×π/180° if Δi has units of degrees)