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Stage 2  Saturn V.

no gravity

Stage 2 — The rocket has already jettisoned the Stage 1 frame and has coasted for 4.4 seconds.

v_exhaust = 4220 m/s

R = 1190 kg/s

t_final = 360 s

m⁰_fuel  = 0.428x10⁶ kg

m_initial = m_final^{Stage 1}— m_jettison^{Stage 1} = 0.73x10⁶ kg — 0.136x10⁶ kg = 0.594x10⁶ kg

m_final  = 0.594x10⁶ kg — 0.428x10⁶ kg = .166x10⁶ kg  =  m_body

v_initial for Stage 2 is v_final of Stage 1—use the Stage 1 result: 3275 m/s—no gravity

**6.5 second coast period between second and third stages;                            displacement given by x_coast = t_coast  v_final

Stage 2 Results and Graphs — no gravity

Let’s dispense with gravity and look at the results if the Saturn V rocket were to be unfettered.

 

 

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Page  5

Data for individual stages.

Stage 2  Notes

v_final =  8650 m/s = 19,300 miles/hour

a(t_initial) = .9 g’s

a(t_final) = 3.1 g’s

x(t_final) = 1950 km = 1210 miles

After the Stage 2 burn, the rocket jettisons 0.0432x10⁶ kg.

Stage 3  Saturn V.

no gravity

Stage 3 occurs in two burns: the first burn puts the rocket into Earth orbit,

the second is the translunar injection.

Let’s live dangerously and burn it all in one go! . . . why not!*

Stage 3 Notes

v_final = 17,100 m/s = 38,200 miles per hour; NASA says the speed at this point would be around 24,500 miles/hour (11,000 m/s).  At this rate the rocket would arrive at the moon in hours, not 3 days!  The reason it takes so long to arrive at the moon is because the rocket slows down.  There’s the influence of gravity again!

a(t_final) = 5.1 g’s — upwards of 10 g’s becomes painful

x(t_final) = 3400 miles

Stage 3 Results and Graphs 

Stage 3 — Total burn 477 seconds. 

v_exhaust = 4630 m/s

R = 216 kg/s

t_final = 477 s

m⁰_fuel  = 0.103x10⁶ kg

m_initial = m_final^{Stage 2}— m_jettison^{Stage 2} = 0.166x10⁶ kg — 0.0432x10⁶ kg = 0.123x10⁶ kg

m_final  = 0.123x10⁶ kg — 0.103x10⁶ kg = 0.020x10⁶ kg = m_body

v_initial for Stage 3 is v_final of Stage 2 — 8650 m/s

*Same results either way.

Page 1

Momentum

Derivation of the Rocket Equation

Thrust

 

Page 2

Speed of the Rocket During the Burn

 

Page 3

Rocket Acceleration

Position as a Function of Time

 

Page 4

Gravity

 

Page 5

Saturn V

Data

Stage 1 Calculation

 

Page 6

Saturn V

Stage 2, Stage 3 Calculations

 

Page 7

Saturn V Photo Gallery

 

Page 8

Saturn V Photo Gallery

 

Page 9

Equation Review

1 Rocket Science

2 Speed

3 Acceleration

4 Gravity

5 Saturn V—Stage 1

6 —Stage 2 —Stage 3

7 Saturn V Photos

8 Saturn V Photos

9 Equation Review

Stage 2 equations – no gravity

Stage 3 equations – no gravity