I've been reading around a lot and I haven't been able to find any clear explanations. Maybe I'm a bit confused or maybe I am just looking in the wrong places.
My question is, what are some basic principles or guidelines to re-entry conditions on a spacecraft? Let's say I have a vehicle in a circular orbit at X km and I perform a retro burn to put my perigee at the tip of Earths atmosphere. Using a blunt-faced capsule design, what are some basic assumptions or relationships I can use to estimate initial velocity, entry angle (corridor bounds), max deceleration, heat flux, etc.? I have found several resources online, however I keep getting wrong numbers from my calculations.
At the very least, could somebody point me in the right direction? Or even explain some concepts I might be lacking? I've dealt with orbital mechanics in the past but this seems like a whole new ball game.
At this point I just need a few numbers to work with (max g load, heat flux and max temp) so that I can use those parameters for material and structural design. Plotting flight profiles will also need to be done however is not a top priority right now.
Here is a worked example for finding max deceleration. According to this FAA PDF, max deceleration can be found using $a_\max = (V^2)*(H*sin(\gamma)) / (2*e)$ where V is initial velocity, H is Earth scale height and $\gamma$ is flight path angle.
So let's say I'm entering Earths atmosphere at 10 km/s and I want a max g load of 8 g's, or 78.48 m/s2. Using this equation, I will need a flight path angle of 1.75 degrees which seems very low to me. The Apollo missions had similar velocities and yet their entry corridor sat at around 7 degrees.