OT - Into the wind in both directions!

wrote in message ...
Rik O'Shea writes:

There's more to wind than is readily apparent. Some of these effects
are shown in an analysis at:

http://www.sheldonbrown.com/brandt/wind.html

W = SQRT((U+V?COS(a))^2+(V?SIN(a))^2)

How does this equation work when the wind speed (V) is greater than
the bicycle speed (U) and the angle of the wind is an obtuse angle
(i.e. tailwind)?

A simple example:

a=180 degree (direct tailwind), U = 20 and V = 19 =
W = 1 which is correct.

However when V is greater than U:

a=180 degree (direct tailwind), U = 20 and V = 21 =
W = 1 which is incorrect.

An example: All the wind speeds and powers are displayed in that item
as continuous curves and the results are not as you suggest. I think
you are ignoring the SIGN which trigonometric functions dutifully
consider. You'll notice that the winds are computed with angle
functions which you have omitted.



I didnt included that info directly (as I thought the sin/cos
associated with 180 degree was apparent).

W = SQRT((U+V?COS(a))^2+(V?SIN(a))^2)

When V is greater than U:

a = 180 degree (direct tailwind)
cos(180) = -1
sin(180) = 0
U = 20
V = 21

W = SQRT((20 + 21*-1)^2 + (21*0)^2)
W = SQRT((-1)^2 + 0)
W = SQRT(1)
W = 1 which is incorrect.

P = U×D×COS(beta)
DoOh, I neglected to include the cosine. I geddit...

Cheers
-R


(Rik O'Shea) wrote in message m...
wrote in message ...
Rik O'Shea writes:

There's more to wind than is readily apparent. Some of these effects
are shown in an analysis at:

http://www.sheldonbrown.com/brandt/wind.html

W = SQRT((U+V?COS(a))^2+(V?SIN(a))^2)

How does this equation work when the wind speed (V) is greater than
the bicycle speed (U) and the angle of the wind is an obtuse angle
(i.e. tailwind)?

A simple example:

a=180 degree (direct tailwind), U = 20 and V = 19 =
W = 1 which is correct.


However when V is greater than U:

a=180 degree (direct tailwind), U = 20 and V = 21 =
W = 1 which is incorrect.

An example: All the wind speeds and powers are displayed in that item
as continuous curves and the results are not as you suggest. I think
you are ignoring the SIGN which trigonometric functions dutifully
consider. You'll notice that the winds are computed with angle
functions which you have omitted.



I didnt included that info directly (as I thought the sin/cos
associated with 180 degree was apparent).

W = SQRT((U+V?COS(a))^2+(V?SIN(a))^2)

When V is greater than U:

a = 180 degree (direct tailwind)
cos(180) = -1
sin(180) = 0
U = 20
V = 21

W = SQRT((20 + 21*-1)^2 + (21*0)^2)
W = SQRT((-1)^2 + 0)
W = SQRT(1)
W = 1 which is incorrect.