Post on 10-Jun-2018
E80 Experimental Engineering
Thrust and Flight Modeling Static Motor Tests and Flight Modeling Lab
Feb. 13, 2014
http://twistedsifter.com/2012/10/red-bull-stratos-space-jump-photos/
E80 Experimental Engineering
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BEM
E80 Experimental Engineering
Outline
• Static Motor Tests and Flight Modeling Lab Overview
• Flight Modeling:
• 1 Degree of Freedom (DOF) Model
• 3 DOF Model
E80 Experimental Engineering
Static Motor Rotation Lab Objectives • Measure the thrust curves, mass flow
rate of combustion gases and
specific impulse for two rocket
motors.
• Construct analytical and 1-D (1 DOF)
and 2-D (3 DOF) numerical models
of rocket flight.
• Compare the analytical and numerical models with the output of
RockSim or OpenRocket.
E80 Experimental Engineering
Where will
the rocket go?
?
E80 Experimental Engineering
Flight modeling
• What key forces dictate the flight trajectory?
E80 Experimental Engineering
The sum of pressure and shear stress is the resultant force. It is split into two components:
1. Lift: The component of resultant force that is perpendicular to the incoming net velocity vector (effective flow direction).
2. Drag: The component of resultant force that is parallel to the incoming net velocity vector (effective flow direction).
Reminder: Lift and Drag
V
E80 Experimental Engineering
One DOF Model:
Free Body Diagram
E80 Experimental Engineering
One DOF Model:
Governing Equation T
..
mz
FD
mg
..
E80 Experimental Engineering
Modeling Thrust
• Is thrust constant during flight?
T
E80 Experimental Engineering
http://v-serv.com/usr/estesmotors.htm
E80 Experimental Engineering
Static Motor Rotation Lab
E80 Experimental Engineering
Static Motor Thrust Curve
http://www.eng.hmc.edu/NewE80/StaticTestVideos.html
E80 Experimental Engineering
Static Motor Lab, Section 2:
• Calculate the total impulse.
• Calculate the average thrust and average mass
flow rate.
• Calculate the exit velocity of the combustion gases
from the nozzle. What assumptions did you have to
make?
• Calculate the specific impulse, Isp.
E80 Experimental Engineering
Drag Force
FD
E80 Experimental Engineering
Analytical One DOF Model
• GE:
mz = T – mg – FD
• Assumptions:
..
E80 Experimental Engineering
Numerical One DOF Model
• GE:
• Many options for numerical solution methods,
e.g.
• OpenRocket uses Runge-Kutta (RK4)
• One option is Explicit Euler ignoring high order terms…
E80 Experimental Engineering
Explicit Euler
E80 Experimental Engineering
One DOF Model
for t = 0 to maxTime
{
T = …
m = …
Fd = …
z_dd(t) = 1/m*(T-m*g-Fd);
z_d(t) = z_d + z_dd*Δt z(t) = z + z_d*Δt }
E80 Experimental Engineering
Three DOF Model
• What are the 3DOF?
Z
X
E80 Experimental Engineering
Why does the rocket rotate?
Wind
Initial
direction
of motion
Wind
Direction of
flow from
rocket motion
New
Direction
of Motion
E80 Experimental Engineering
Reminder: Angle of Attack
E80 Experimental Engineering
Angle of Attack
E80 Experimental Engineering
Three DOF Free Body Diagram
..
θ
CG
CP
α
z
x
E80 Experimental Engineering
Non-Rotational Forces
• z-direction
• x-direction
z
x
..
..
T
..
mz
FD
mg
..
mx
θ
E80 Experimental Engineering
Torque Balance
V
α TD
CG
CP
L
..
Iθ
E80 Experimental Engineering
Rotational Damping
• The rotational damping can be modeled as
.
.
E80 Experimental Engineering
Rocket Stability
• Is this stable?
• Depends on location of CP versus CG
V
α
CG
CP
L
V
α
CG
CP
L
E80 Experimental Engineering
Reminder: Complication #3 Angle of Attack
CL,CD = f(α, Re)
E80 Experimental Engineering
Drag and Lift direction
• Drag and lift can be defined w.r.t.
θ
CG
CP
α
θ
CG
CP
α
Rocket axis Effective flow direction
E80 Experimental Engineering
Three DOF Model
for t = 0 to maxTime
{
T = …
m = …
Fd = …
L = …
Td = …
alpha = …
z_dd(t) = …
x_dd(t) = …
θ_dd(t) = …
…
}
E80 Experimental Engineering
To Linde Field
• Good luck!