Entry Dynamics

Atmospheric Entry

The atmospheric entry phase starts at about 100 km where the atmosphere slowly becomes more noticeable. The atmospheric entry is a phase of high decelerations and high thermal loads. Generally speaking, there are two major types of entry vehicles: ballistic vehicles or lift generating vehicles. 

Ballistic entry vehicles

Ballistic vehicles are vehicles that do not generate lift and thus follow a ballistic trajectory. These types of vehicles include the Russian Vostok, and Voshkod crewed capsules. A similar entry body can be found in the current Foton, unmanned, capsules. Other ballistic re-entries can be found in sample return missions, where one can also see the very high decelerations and thermal loads. The flight path of a ballistic entry can be modelled using the following equation:

Ballistic Entry

When rearranging the equation, one can write it as velocity, V,  over density, ρ (density typically being a function of the altitude). Then one can see that the velocity is mainly governed by the entry conditions: entry velocity (VE) and entry angle (γE). The second parameter of influence is the ballistic coefficient, K. The ballistic coefficient can be seen as the entry vehicle's aerodynamic performance and is defined as K = M/Cd*A. The remaining coefficients g and β are the gravitational acceleration and the inverse of the scale height. 

The figures below show the influence of the ballistic coefficient and entry angle when the vehicle enters the atmosphere at an altitude of 100 km with a velocity of 7 km/s.  As can be seen in the figure on the left, a higher ballistic coefficient causes the location of peak deceleration to be shifted upwards in altitude. The effect of the entry angle is much less significant, as can be seen on the right. Besides the deceleration, the ballistic coefficient also influences the terminal velocity of the vehicle. A lower terminal velocity will, in most cases, lead to a lower load on the parachute during parachute inflation. 

Lift generating entry vehicles

Some vehicles entering the atmosphere generate lift and are thus categorised as lift generating vehicles. There are quite some examples of this type of vehicles, such as the Space Shuttle, Buran, IXV, and Space Rider. Lift generating vehicles are generally more complex then ballistic vehicles but tend to have much lower peak decelerations. The increased complexity originates in stricter shape and aerodynamic requirements, leading to more complex structures and control subsystems. The velocity-altitude of a lift generating vehicle can be found below:

The velocity equation of a lift generating vehicle is a function of the air density and the factor comparable to the ballistic coefficient. This parameter, K2, is defined as K2 = (W/S)/CL. The influence of the K2 factor can be seen in the figure on the right. In this equation, the vehicle's weight is W in Newtons, S is the wing area in m2 and CL is the vehicle's lift coefficient. The parameter Vc,0 is the local circular velocity at entry.

Apollo 11 re-entry trajectory

Planned re-entry trajectory of Apollo 11

Some lift-generating vehicles are not as obvious as the Space Shuttle. As an example, the Apollo capsule had a non-zero lift by offsetting the centre of pressure and centre of gravity. This meant that, even though the vehicle does not have wings, it can still control the flight path. As a matter of fact, most crewed capsules have the ability to generate lift to reduce the re-entry loads. Apollo used this capability during the entry to bleed off as much velocity as possible before deploying the parachutes. The planned entry trajectory of Apollo 11 can be seen on the left as can be seen the vehicle levels off after the first deceleration peak. This allows for the total deceleration and heat loading to be distributed over a longer time and trajectory, decreasing the peak loadings. 

When directing this lift upward, the capsule can deflect its velocity vector from downward to upward. When this is done sufficiently, the capsule can exit the atmosphere again. This is called skipping entry. Skipping entries have been done on the Russian Zond missions and the Chinese Chang'e 5-T1 mission. During Artemis 1, Orion also performed a skipping entry. This marked the first time a crew-rated capsule performed such a feat.