Calculating Maximum Deceleration of Re-entry Capsule

In summary, the maximum deceleration experienced by the re-entry capsule will be 243.122 m/s^2 at an altitude determined by the BC number. The correct calculation is 7400^2 (0.000139m^-1 sin(10)) / 2 = 24.813 m/s^2.
  • #1
spacemike1
5
0

Homework Statement




Contact lenses being manufactured in space are returned in a re-entry capsule to Earth for distribution and sale. If the re-entry velocity is 7.4km/s and the re-entry flight-path angle is 10 degrees, determine the maximum deceleration it will experience and at what altitude? The capsule’s BC is 1000 kg/m^2

Homework Equations



a max = V^2 re-entry b sin y/ 2e


The Attempt at a Solution



a max = 7400m/s^2 (0.000139m^-1 sin(10)) / 2(2.7182)

the answer should be 24.813 , I keep getting a very high number of 9.298x10^10 ... why am I so off?

where .000139m^-1 is the atmospheric scale height and 2.7182 is the base of the natural logarithm.
 
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  • #2
When I run the same numbers I get 243.122 m/s^2

Where does the BC number figure into the problem?
 
  • #3
the BC number is actually for the second part of the question. You got closer to me. I tried my calcs again and still getting the same off-base number. I've plugged it into the calculator just like this.

7400^2 (0.000139m^-1 sin(10)) / 2(2.7182) and get 9.298x10^10
 
  • #4
You apparently are dividing by 0.000139m^-1.
 
  • #5
D H said:
You apparently are dividing by 0.000139m^-1.

...and multiplying by e.
 

1. What is the purpose of calculating maximum deceleration of a re-entry capsule?

The purpose of calculating maximum deceleration of a re-entry capsule is to determine the maximum force or acceleration that the capsule will experience during the re-entry process. This information is crucial for ensuring the safety and stability of the capsule and its occupants.

2. How is maximum deceleration of a re-entry capsule calculated?

Maximum deceleration of a re-entry capsule is typically calculated using the formula a = v^2/R, where "a" is the maximum deceleration, "v" is the velocity of the capsule, and "R" is the radius of the Earth. This formula takes into account the speed and curvature of the Earth's surface and allows for a more accurate calculation of deceleration.

3. What factors affect the maximum deceleration of a re-entry capsule?

The maximum deceleration of a re-entry capsule can be affected by several factors, including the speed and angle of re-entry, the shape and design of the capsule, and the atmospheric conditions. The weight and mass distribution of the capsule can also play a role in determining its maximum deceleration.

4. How does maximum deceleration impact the design of a re-entry capsule?

The maximum deceleration of a re-entry capsule is a crucial factor in the design process. The capsule must be able to withstand the calculated deceleration forces in order to ensure the safety of the occupants. This may require the use of specialized materials and structural design to withstand the high levels of stress.

5. Are there any safety measures taken to reduce the maximum deceleration of a re-entry capsule?

Yes, there are several safety measures that can be taken to reduce the maximum deceleration of a re-entry capsule. These may include using heat shields or other protective materials to minimize the effects of atmospheric friction, as well as carefully planning the trajectory and angle of re-entry to avoid excessive deceleration forces. Additionally, the capsule may be equipped with parachutes or other braking mechanisms to slow down its descent and reduce the maximum deceleration experienced.

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