Transcript Drag

Drag and Lift
E80 Fluid Measurements
Spring 2009
Forces on a Rocket
http://www.grc.nasa.gov/WWW/K-12/rocket/rktfor.html
The Question
• In the event of a crash landing of your
rocket, what will be the effect on the
instruments inside the rocket?
(Translation)
• What is the velocity of impact?
• What is the impulse response of the
rocket structure?
Aerodynamic Forces
What force does a moving fluid exert on a solid
body immersed in the fluid?
At any point on surface:
Fn  P A P : pressure
Ft   A  : shear stress
Aerodynamic Forces
Integrate pressure and shear stress
distributions around body surface
Drag FD - component of resultant force in
direction of flow
Lift FL - component of resultant force
perpendicular to direction of flow
The Wind Tunnel
LVDT Displacement Sensors
http://www.macrosensors.com/lvdt_macro_sensors
Pitot Static Tube
Venturi Effect
 A1V1   A2V2 (mass balance)
P1  12 V12  P2  12 V22
(energy balance for isentropic flow)
P1  P2  gh (static force balance)
http://en.wikipedia.org/wiki/Venturi_effect
One Dimensional Flow
 AV  constant  m (mass flowrate)
P  12 V 2  constant  P0
( Bernoulli ' s Equation)
( static pressure  dynamic pressure  total pressure)
Pitot Static Tube
• At A PA  P  12 V 2
• At B PB  P
V 
2  PA  PB 

Newton’s Hypothesis
“Pressure” Drag
FD  ApV 2
Viscous Boundary Layer
 dV 
“Skin Friction” Drag FD  As   dy  dA

s
Dimensional Analysis
FD  f   ,V ,  , L 
or
g  FD ,  , V ,  , L   0
• 5 variables, 3 dimensions
(mass,length,time) => 2 dimensionless
groups
Dimensional Analysis
 FD
 
g
,
0
2 2
 V L VL 
Define:
Drag Coefficient
Reynolds Number
FD
CD  1
2
2 V Ap
VL
Re 

Dimensional Analysis
CD  f  Re 
Similarly define:
Lift Coefficient
FL
CL  1
2
2 V Ap
CL  f  Re 
Cd Values
Lift Coefficient of Airfoil
http://www.aquaphoenix.com/lecture/ideas-flow/
Wave Drag
http://aerorocket.com/VisualCFD/IMAGES/
The Wind Tunnel
Pitot Calibration
V
2P

?
P (inches H 2 0)
  f T , P,humidity
Drag and Lift Measurements
CD 
CL 
FD
1
2
V Ap
2
FL
1
2
V Ap
2
?
?
VL
Re 
?

  f (T )
E80 Fluid Measurements Lab
1. Calibrate Wind Tunnel Pitot Tube
2. Measure Drag Coefficient of Two Spheres
(smooth surface, rough surface). Compare
to Literature Values
3. Measure Drag and Lift Coefficients for
scaled rocket as a function of angle of
attack. Compare to Literature Values
4. Calibrate the pitot tube on the nose cone of
your rocket.
5. Estimate the impact velocity of your rocket.