p.s. Assuming free space.
You can play around with a great freeware program called 4NEC2, which makes it really easy to model any antenna over any kind of ground (or none)
Eric
Is that a quarter wave per leg or total? A 1/2 wave vee has a pattern nearly identical to a dipole. On the third harmonic, you'll have additional major lobes.
I just happen to be in the process of writing a book for the ARRL dedicated specifically to radio propagation, especially ionospheric.
But, you've had some good answers here, as ionospheric refraction is a very MACRO phenomenon. The ionosphere, as a whole has a very large "radar cross-section"...
My latest science project has required that I invest in some surface mount soldering equipment. I figured I was going to be old, blind, and dead before I had to do this stuff. Turns out I'm a lot better at this than most electronics whippersnappers. :)