Rocket Build Project

Boost Velocity

Terminal Velocity

Max Altitude

Drag Modeling

Flight Testing

MAE 2

2MAE 2

Rocket Project

Two-person teams will design, build, and fly a compressed-air launch vehicle.

Use flight test video to validate trajectory predictions.

Project Design Report

Due FRI 31 OCT 2014

10% of final course grade

4-page maximum length

Content

Configuration Sketches

Design Calculations

Documented Flight Performance

3MAE 2

Boost Velocity

The boost velocity is the velocity achieved when the rocket motors cut off.

V b=2 f Tmg

TPd /22

V b=boost velocityf =fuselage length

T=thrustW=weightm=massg=gravity

T=thrust=piston efficiency 0.010.02

P=air tank pressured=fuselage diameter

T

W=mg

Note: Drag force is ignored during boost phase.

center-of-gravity

4MAE 2

Terminal Velocity

The terminal velocity is found during descent, when the drag force is exactly balanced by weight.

B= mS CD

B=ballistic parameterm=mass

S=reference areaCD=drag coefficient

D

W=mg

center-of-gravity

mg=W=D=12V 2 S CD V= 2 g mSCD

V t= 2 g BV t=terminal velocityg=gravity=density

5MAE 2

Maximum Altitude

The maximum altitude of the rocket is found at the point where the rocket stops climbing -- which means that its velocity is zero.

The maximum altitude expression depends on the boost velocity as well as the terminal velocity.

hmax=V t

2

2 g ln [V t2V b2V t2 ]hmax=maximum altitude

g=gravityV t=terminal velocityV b=boost velocity

6MAE 2

4 6 8 10 12 14 160

2

4

6

8

10

12

Design for Maximum Altitude

Boost Velocity (m/s)

Max

imum

Alti

tude

(m)

B = 60 kg/m2

B = 20 kg/m2

B = 40 kg/m2

7MAE 2

Total Drag Summary

The ballistic coefficient depends on the rocket drag characteristics.

S CD=D fusq all fins

D finq

The drag coefficient is found by estimating contributions from the fuselage and tail fins.

B= mSC D

q=12V 2=dynamic pressure

8MAE 2

Fuselage Drag

D fus=fuselage dragd=fuselage diameterf =fuselage length

= f /d=fineness ratioq=dynamic pressure

D fusq =Cd

d2

2

McCormick, B.W., Aerodynamics, Aeronautics, and Flight Mechanics, Wiley, 1979.

9MAE 2

Tail Fin Drag

The drag from tail fins comes mainly from skin friction.

D finq 0.02S fin

S fin=wing fin areaS=reference areaAR=aspect ratio

b=spancr=root chordct=tip chord

b

ct

cr

AR=b2

S= 2bcrct

S= b2crct Note: Use S/2 as the area of a single fin.

10MAE 2

Drag Build Up Example

Fuselage:

D fusq =0.28 cm

2

Tail Fin:

S CD=D fusq all fins

D finq =0.2840.15

D finq 0.02S fin

D fusq 0.08

d2

2d=2.1cm

S fin=7.5cm2 D fin

q =0.15cm2

Total (with 4 tail fins):

S CD=0.88cm2

Ballistic Parameter:

B=45 kgm2B=

mSCD

= 4 g0.88cm2 1002cm2

m2 kg1000 g m=4grams

11MAE 2

Static Stability for a Rocket

unstablewithout fins

stablewith fins

Queijo, M.J., and Michael, W.H., Wind-Tunnel Investigation of the Low Speed Static Stability and Control Characteristics of A Model of Bell MX-776, NACA Report RM SL9G08, 1949.

12MAE 2

Rocket Design Summary

A high boost velocity is needed to maximize altitude.

High propulsion efficiency (eta)

Long fuselage

Low mass

A large ballistic parameter reduces the rate of deceleration in coast phase.

High mass

Low drag

Small area tail fins

Fuselage length about four times the fuselage diameter

Static stability is needed to insure a smooth vertical flight path.

13MAE 2

Analytical Predictions

Record air pressure before launch; then use the pressure to estimate thrust.

V b=2 f Tmg

B= mSCD

V t= 2 g B hmax= V t2

2 g ln [V t2V b2V t2 ]

TPd /22

Use weight scale to get the rocket's mass; then estimate boost velocity.

Estimate drag characteristics; then compute ballistic parameter.

Compute terminal velocity and maximum altitude.

f =fuselage lengthm=rocket mass

T= thrust=piston efficiency 0.015

P=air tank pressured=fuselage diameter

14MAE 2

Test Flight Data

The boost velocity is found just after the rocket leaves the launch tube.

The terminal velocity is found just before the rocket lands or crashes.

The maximum altitude is found by counting the number of bricks from the launch point to the highest point in the flight.

V number of bricks number of movie frames 6 inchesbrick feet12 inches 120 framessec

hmax total number of bricks 6 inchesbrick feet12 inches units: ft

units: ft/sec

15MAE 2

Resources

NASA Rocket Modeler III

http://www.grc.nasa.gov/WWW/K-12/rocket/rktsim.html

Kerbal Space Program

https://www.kerbalspaceprogram.com/index.php

Open Rocket

http://openrocket.sourceforge.net/

http://www.grc.nasa.gov/WWW/K-12/rocket/rktsim.htmlhttps://www.kerbalspaceprogram.com/index.phphttp://openrocket.sourceforge.net/Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15