Solution 7.106
Since the only unknown is the kite area, this problem is simpler than Prob. P7.85. Convert
Problem 7.107
The largest flag in Rhode Island stands outside Herb Chambers’ auto dealership, on the edge of
Route I-95 in Providence. The flag is 50 ft long, 30 ft wide, weighs 250 lbf, and takes four
strong people to raise it or lower it. Using Prob. P7.40 for input, estimate (a) the wind speed, in
mi/h, for which the flag drag is 1000 lbf; and (b) the flag drag when the wind is a low-end
category 1 hurricane, 74 mi/h. [HINT: Providence is at sea level.]
Problem 7.40
Hoerner [12, p. 3.25] states that the drag coefficient of a flag in winds, based on total wetted area
2bL, is approximated by CD ≈ 0.01 + 0.05L/b, where L is the flag length in the flow direction.
Test Reynolds numbers ReL were 1 E6 or greater. (a) Explain why, for L/b ≥ 1, these drag values
are much higher than for a flat plate. Assuming sea-level standard air at 50 mi/h, with area
bL = 4 m2, find (b) the proper flag dimensions for which the total drag is approximately 400 N.
Solution 7.107
Prob. P7.40 suggests a drag coefficient CD 0.02 + 0.1(L/b), based on flag area Lb. Thus, for
kite
Problem 7.108
The data in Fig. P7.108 are for lift and drag of a spinning sphere from Ref. 45. Suppose a tennis
ball (W 0.56 N, D 6.35 cm) is struck at sea level with initial velocity Vo = 30 m/s, with
“topspin” (front of the ball rotating downward) of 120 rev/sec. If the initial height of the ball is 1.5 m,
estimate the horizontal distance travelled before it strikes the ground.
22
Solution 7.108
Problem 7.109
The world record for automobile mileage, 12,665 miles per gallon, was set in 2005 by the PAC-
CAR II in Fig. P7.109, built by students at the Swiss Federal Institute of Technology in Zurich
[52]. This little car, with an empty weight of 64 lbf and a height of only 2.5 ft, traveled a 21-km
course at 30 km/hr to set the record. It has a reported drag coefficient of 0.075 (comparable to an
airfoil), based upon a frontal area of 3 ft2. (a) What is the drag of this little car when on the
course? (b) What horsepower is required to propel it? (c) Do a bit of research and explain why a
value of miles per gallon is completely misleading in this particular case.
Solution 7.109
For air, assuming sea-level, take
= 0.00238 slug/ft2. Convert V = 30 km/h to 27.34 ft/s.
(a) Then the car’s drag on the course, in lbf, is
Problem 7.110
A baseball pitcher throws a curveball with an initial velocity of 65 mi/h and a spin of 6500 r/min
about a vertical axis. A baseball weighs 0.32 lbf and has a diameter of 2.9 in. Using the data of
Fig. P7.108 for turbulent flow, estimate how far such a curveball will have deviated from its
straightline path when it reaches home plate 60.5 ft away.
Solution 7.110
For sea-level air, take
= 0.00238 slug/ft3 and
= 3.72E−7 slug/fts. Again, for this short
distance, the ball travels
Problem 7.111*
A table tennis ball has a mass of 2.6 g and a diameter of 3.81 cm. It is struck horizontally at an
initial velocity of 20 m/s while it is 50 cm above the table, as in Fig. P7.111. For sea-level air,
what spin, in r/min, will cause the ball to strike the opposite edge of the table, 4 m away? Make
an analytical estimate, using Fig. P7.108, and account for the fact that the ball decelerates during
flight.
Solution 7.111
For sea-level air, take
= 1.225 kg/m3 and
= 1.78E−5 kg/ms. This problem is difficult
because the ball is so light and will decelerate greatly during its trip across the table. For the last
time, as in Prob. 7.108, for this short distance, we assume the ball travels in nearly a circular arc,
Problem 7.112
A smooth wooden sphere (SG = 0.65) is connected by a thin rigid rod to a hinge in a wind
tunnel, as in Fig. P7.112. Air at 20C and 1 atm flows and levitates the sphere. (a) Plot the angle
versus sphere diameter d in the range 1 cm d 15 cm. (b) Comment on the feasibility of this
configuration. Neglect rod drag.
Solution 7.112
For air, take
= 1.2 kg/m3 and
= 1.8E−5 kg/ms. If rod drag is neglected and
L d,
the
balance of moments around the hinge gives:
Problem 7.113
An automobile has a mass of 1000 kg and a drag-area CDA = 0.7 m2, The rolling resistance of
70 N is approximately constant. The car is coasting without brakes at 90 km/h as it begins to
climb a hill of 10 percent grade (slope = tan-1 0.1 = 5.71). How far up the hill will the car come
to a stop?
Solution 7.113
For sea-level air, take
= 1.225 kg/m3 and
= 1.78E−5 kg/ms. If x denotes uphill, the equation
of motion is
Problem 7.114
The deep submergence vehicle ALVIN is 23 ft long and 8.5 ft wide. It weighs about 36,000 lbf
in air and ascends (descends) in the seawater due to about 360 lbf of positive (negative)
buoyancy. Noting that the leading face of the ship is quite different for ascent and descent,
(a) estimate the velocity for each direction, in meters per minute. (b) How long does it take to
ascend from its maximum depth of 4500 m?
Solution 7.114
Well, nothing in Table 7.3 looks much like the top or the bottom of ALVIN. Let’s just estimate.
When ascending, the leading face of ALVIN is cluttered and ugly and approximates a blunt
Problem 7.115
The Cessna Citation executive jet weighs 67 kN and has a wing area of 32 m2. It cruises at
10 km standard altitude with a lift coefficient of 0.21 and a drag coefficient of 0.015. Estimate
(a) the cruise speed in mi/h; and (b) the horsepower required to maintain cruise velocity.
Solution 7.115
At 10 km standard altitude (Table A-6) the air density is 0.4125 kg/m3.
Problem 7.116
An airplane weighs 180 kN and has a wing area of 160 m2 and a mean chord of 4 m. The airfoil
properties are given by Fig. 7.25. If the plane is designed to land at Vo = 1.2Vstall, using a split
flap set at 60, (a) What is the proper landing speed in mi/h? (b) What power is required for
takeoff at the same speed?
Solution 7.116
For air at sea level,
1.225 kg/m3. From Fig. 7.24 with the flap, CL,max 1.75 at
6.
Compute the stall velocity:
Problem 7.117
The Transition® auto-car in Fig. 7.30 has a weight of 1200 lbf, a wingspan of 27.5 ft, and a wing
area of 150 ft2, with a symmetrical airfoil, CD = 0.02. Assume that the fuselage and tail section
have a drag-area comparable to the Toyota Prius [21], CDA 6.24 ft2. If the pusher propeller
provides a thrust of 250 lbf, how fast, in mi/h, can this car-plane fly at an altitude of 8200 ft?
Solution 7.117
From Table A.6, at 8200 ft = 2500 m, air density is 0.957 kg/m3 = 0.00186 slug/ft3. The wing
has an aspect ratio AR = (27.5 ft)2/(150 ft2) = 5.04. The wing lift and drag coefficients are
Problem 7.118*
Suppose the airplane of Prob. 7.116 is now fitted with all the best high-lift devices of Fig. 7.28.
(a) What is its minimum stall speed in mi/h? (b) Estimate the stopping distance if the plane lands
at Vo = 1.25Vstall with constant CL = 3.0 and CD = 0.2 and the braking force is 20 percent of the
weight on the wheels.
Solution 7.118*
For air at sea level,
= 1.225 kg/m3. From Fig. 7.28 read CL,highest 4.0.
Problem 7.119
A transport plane has a mass of 45,000 kg, a wing area of 160 m2, and an aspect ratio of 7.
Assume all lift and drag due to the wing alone, with CD = 0.020 and CL,max = 1.5. If the aircraft
flies at 9,000 m standard altitude, make a plot of drag (in N) versus speed (from stall to 240 m/s)
and determine the optimum cruise velocity (minimum drag per unit speed).
Solution 7.119
From Table A.6, at 9000 m,
= 0.4661 kg/m3. First compute the stall velocity:
Problem 7.120
Show that, if Eqs. (7.70) and (7.71) are valid, the maximum lift-to-drag ratio occurs when
CD = 2CD. What are (L/D)max and
for a symmetric wing when AR = 5.0 and CD = 0.009?
Solution 7.120
According to our lift and induced-drag approximations, Eqs. (7.70) and (7.71), the lift-to-drag
ratio is
Problem 7.121
In gliding (unpowered) flight, lift and drag are in equilibrium with the weight. Show, that, if
there is no wind, the craft sinks at an angle tan θ drag/lift. For a sailplane of mass 200 kg, wing
area 12 m2, and aspect ratio 11, with an NACA 0009 airfoil, estimate (a) the stall speed, (b) the
minimum gliding angle, and (c) the maximum distance it can glide in still air when it is 1200 m
above level ground.
Solution 7.121
By the geometry of the figure, with no thrust, wind, or acceleration,
Problem 7.122
A boat of mass 2500 kg has two hydrofoils, each of chord 30 cm and span 1.5 m, with
CL,max = 1.2 and CD = 0.08. Its engine can deliver 130 kW to the water. For seawater at 20C,
estimate (a) the minimum speed for which the foils support the boat, and (b) the maximum speed
attainable.
Solution 7.122*
For seawater at 20C, take
= 1025 kg/m3 and
= 0.00107 kg/ms. With two foils, total
planform area is 2(0.3 m)(1.5 m) = 0.9 m2. Thus the stall speed is