First, let's talk overheating. Where is the heat coming from? How does it go away? The heat is coming from friction (1). Friction is converting your speed into heat. Your craft is absorbing (2) the heat of that friction. In other words, the faster you are de-accelerating (3), the faster you accumulate heat Your craft also radiates (4) heat. This heat radiation is based on the difference between the ambient temperature and the heat of your craft. In other words, the hotter you are, the faster you dump heat. Radiators increase that rate of transfer, but it's still a factor of temperature difference. As long as your radiators are hotter than the air around them, they will be dumping heat. Hint: Keep them out of the airstream, since the friction heats the air at the point of contact. So, to keep from exploding because of heat, you want to slow down your heat accumulation, by reducing your rate of de-acceleration. How do you slow down slower, over a longer period of time? Shallow re-entry, where most of your speed is horizontal, rather than vertical. You want to go round and round Kerbin until you are going slowly, rather than plunging straight towards the center of the world. Simple way of doing that is have your perapsis between 28k and 32k meters above the surface when you hit the atmosphere. Aim to miss Kerbin, not hit Kerbin. Ok, so now we have your craft re-entering the atmosphere in such a way that it doesn't explode from heat, and has plenty of time to slow down. You want to have enough parachutes so you are travelling under 7m/s when you touch down. I've found that means 1 kg of parachute for every 15 kg of craft, or 0.1 tons of chute (one radial chute) for every 1.5 tons of empty weight. When do you deploy? When your speed is below 250 m/s. With the shallow re-entry profile, most of my craft get below 250 m/s by 6000m off the ground. Depends on how aerodynamic your craft is. If you need more drag, consider air brakes or landing struts - extending them will increase your drag. Deploy them after all the flaming graphics have stopped, to keep them from burning off. tl:dr: 1 radial chute for every 1.5 tons of craft. Set your perapsis for 30km. Deploy your landing gear after the flames have died down. Deploy the chutes after your speed is below 250 m/s. (1) And compression. Ignoring compression as it adds complexity without actually changing the answer (2) Part of that heat goes to atmo, part to the craft. Simplified because it doesn't actually change anything (3) And travelling, due to compression heat. Ignoring that component because. (4) Radiation and conduction (I don't think convection is modeled). Simplified.
