As per the clause 7.1 Device Use Zone in The ASTM F2970 Standard, the device use zone shall comprise the area from the ground surface underneath the TC beds to 204 in. (518.16 cm) above the ground surface. So the minimum clear height (from the ground to the lowest obstacle in roof space) should be 204 in. (518.16 cm) . For you information, it is required 5.2m minimum in PAS 5000 (British Standard). Generally we would recommend the minimum clear height to be 5.2m. 

If there's high performance trampoline (also called professional trampoline), the height requirement depends on the web mat. It requires 6.2m clear height for 13mm web mat, and 7.7m for 6mm web mat. For Pokiddo trampoline park with high performance mat, we would require the space to be 6.2m minimum.