Originally Posted by
Vessbot
Yes, there will be, for the reason explained by the math I posted.
What's the groundspeed before the turn? -499
What's the groundspeed after the turn? 501
The difference is 1000.
I read your post again, and it still rearranges the terms in error. Look at scenario A, and see that obviously everything is right. This is common sense to a private pilot. And then look at how every element translates to scenario B. Have I made any mistakes in the translations?
The difference between these two examples is that in one the windspeed is less than the airspeed and in the other the windspeed is greater than the airspeed. In both cases airspeed is positive. In the first case the groundspeed reverses direction and in the second case the groundspeed is in the same direction. That means that in the first case you are entitled to take the difference between the groundspeeds but in the second case you have to take the sum. In other words along with common sense there is a minus sign missing.
I don't really mind where you stick it.
I should add that this is because calculation of groundspeed is a triangle of velocities problem envolving the cosine of the wind-angle. Less than 90 degrees is positive Greater than 90 degrees is negative
(1+500)+(1-500)
=501 +(-499)
=2