How big is your backyard? I found this by googling "backyard halfpipe":
The skaters may be a resource for construction ideas.
I'm thinking anything much shorter than 150m would require "wall of death" banking. Perhaps two turns of 16m inside radius and two 25m straights to connect to get a 150m track.
For the space it might require, figure 5m wide track surface, so we get width of 5+16+16+5=42m and for length add 25m to that figure to get 67m, so 67mX42m or so.
How much land is that? I'm thinking it's about 3/4 of an american acre. I'm guessing the pictured halfpipe is taking up less than 1/4 of that space.
Doe this sound about right?