Consider a hill and a ridge as illustrated in the figure below. Both the hill and ridge have a semi-circular xz cross-section of radius R, and the wind is blowing in the x direction with speed V∞.

Question

To allow sustained flight with no thermals present, a sailplane must be flown in the region above the hill or ridge where the vertical velocity component is at least 1m/s.

Hint: For the following questions, be sure to include max-thickness corrections for the doublet strengths. See sections 2.11.3 and 2.12.2 in the textbook.

Use the following case-sensitive typed names for the various symbols.

Symbol

x

y

z

R

V∞

π

Typed

x

y

z

R

V

pi

HILL (1 point possible)
1) Determine the sustained-flight region for the hill, defined by f(x,y,z,R)>1, when the far-away wind speed is V∞=12m/s.

f(x,y,z,R)=2 - incorrect
2
You have used 2 of 2 submissions
RIDGE (1 point possible)
2) Determine the sustained-flight region for the ridge, defined by g(x,z,R)>1, when the far-away wind speed is V∞=12m/s.

g(x,z,R)=- unanswered
You have used 0 of 2 submissions
SUSTAINABLE FLIGHT (4 points possible)
3) Sailplane pilots like to have available the largest possible vertical air velocities. Would the pilot prefer to fly near the isolated hill or the ridge?

Hill<text> Hill</text> - incorrectRidgeBoth are equally attractiveThere is no basis for decision
4) For the hill, what is the minimum wind speed below which the glider cannot sustain flight anywhere? Round your answer to two decimals.

0 - incorrect
0
5) For the ridge, what is the minimum wind speed below which the glider cannot sustain flight anywhere? Round your answer to two decimals.

0 - incorrect
0
6) If the radius R of the hill or ridge were increased, how would the minimum wind speed be affected?

Minimum wind speed would decrease<text> Minimum wind speed would decrease</text> - incorrectMinimum wind speed would increaseMinimum wind speed would be unaffectedThere is no basis for decision