Chapter 10 - Dynamic lift

Example 2a - Pg 427

In [1]:
#calculate the max. theoretical propulsive force
#Initialization of variables
import math
vel=50. #mph
w=240. #rpm
r0=3. #ft
L=30. #ft
rho=0.00230 #slug/ft^2
theta=30*math.pi/180. #radians
#calculations
V=vel*5280./3600.
T=2*math.pi*r0*r0 *w*2*math.pi/60.
Fl=rho*V*T*L
F=r0*Fl*math.cos(theta)
#results
print '%s %d %s' %("Max. theoretical porpulsive force =",F,"lb")
print '%s' %("The answers are a bit different from textbook due to rounding off error")

Max. theoretical porpulsive force = 18683 lb
The answers are a bit different from textbook due to rounding off error

Example 2b - Pg 428

In [2]:
#calculate the force required for the operation
#Initialization of variables
import math
vel=50. #mph
w=240. #rpm
r0=3. #ft
L=30. #ft
rho=0.00230 #slug/ft^2
theta=30*math.pi/180. #radians
Cl=2
Cd=1
#calculations
vc=r0*w
V=vel*5280./3600.
vr=vc/V
A=2*r0*L
Fl=Cl*A*0.5*rho*V*V 
Fd=Cd*A*0.5*rho*V*V
F=r0*(Fl*math.cos(theta) + Fd*math.sin(theta))
#results
print '%s %d %s' %("Force required =",F,"lb")
print '%s' %("The answers are a bit different from textbook due to rounding off error")

Force required = 7454 lb
The answers are a bit different from textbook due to rounding off error

Example 3a - Pg 432

In [4]:
#calculate the boundary circulation
#Initialization of variables
W=7500 #pounds
rho=0.00230
V=175*5280/3600 #ft/s
B=50
#calculations
T=W/(rho*V*B)
#results
print '%s %d %s' %("Boundary circulation =",T,"ft^2/s")

Boundary circulation = 254 ft^2/s

Example 3b - Pg 433

In [5]:
#calculate the horsepower required for the operation
#Initialization of variables
W=7500. #pounds
rho=0.00230
V=175*5280./3600. #ft/s
B=50.
A=350. #ft^2
#calculations
Cl=W/(A*0.5*rho*V*V)
Cd=0.03
Fd=Cd*A*0.5*rho*V*V 
hp=Fd*V/550.
#results
print '%s %d %s' %("Horsepower required =",hp,"hp")

Horsepower required = 371 hp

Example 4 - Pg 437

In [6]:
#calculate the horsepower required for the operation
#Initialization of variables
import math
Fl=7500. #pounds
rho=0.00230
V=175*5280./3600. #ft/s
B=50
A=350 #ft^2
#calculations
Vi=2*Fl/(math.pi*rho*V*B*B)
Cl=Fl/(A*0.5*rho*V*V)
Cdi=Cl*Vi/(V)
Fdi=Cdi*A*0.5*rho*V*V
hp=Fdi*V/550
#results
print '%s %.1f %s' %("Horsepower required =",hp,"hp")

Horsepower required = 44.1 hp