Chapter 11 The coeﬃcient of lift is speciﬁed by the data on Fig

11.64: PROBLEM DEFINITION

Situation:

An airplane wing has a chord of 3.5 ft. Air speed is Vo=200ft/s.

Theliftis1800lbf. Theangleofattackis3

o.

The coeﬃcientofliftisspeciﬁed by the data on Fig. 11.24 in EFM10e.

Find: The span of the wing.

Properties: Density of air is 0.0024 slug/ft3.

PLAN

Guess an aspect ratio, look up a coeﬃcient of lift and then calculate the span. Then,

iterate to ﬁnd the span.

SOLUTION

Lift force. From Fig. 11.24 (EFM10e) assume CL≈0.60.Then

From Fig. 11.24 (EFM10e), CL=0.50.Recalculate the span

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11.65: PROBLEM DEFINITION

Situation: A lifting vane for a boat of the hydrofoil type is described in the problem

statement.

Find: Dimensions of the foil needed to support the boat.

SOLUTION

Use Fig. 11.24 (in EFM10e) for characteristics; b/c =4so CL=0.55

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11.66: PROBLEM DEFINITION

Situation: Two wings, A and B, are described in the problem statement.

Find: Total lift of wing B compared to wing A.

SOLUTION

80

11.67: PROBLEM DEFINITION

Situation: An aircraft increases speed in level ﬂight.

Find: What happens to the induced drag coeﬃcient.

SOLUTION

Intheequationfortheinduceddragcoeﬃcient (above) the only variable for a given

airplane is CL; therefore, one must determine if CLvaries for the given conditions. If

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11.68: PROBLEM DEFINITION

Situation: An airplane wing is described in the problem statement.

Find:

(a) An expression for Vfor which the power is a minimum.

(b) Vfor minimum power

SOLUTION

For minimum power dP/dV =0so

For ρ=1kg/m3,Λ=10,W/S=600and CDo =0.2

82

11.69: PROBLEM DEFINITION

Situation:

An airstream aﬀected by the wing of an airplane is described in the problem state-

ment.

Find:ShowthatCDi =C2

L/(πΛ).

SOLUTION

Take the stream tube between sections 1 and 2 as a control volume and apply the

momentum principle

For steady ﬂow the momentum equation is

But the ﬂuidactingonthewingintheydirection is the lift FLand it is the negative

of Fy.So

Eliminate FLbetween the two equations yields

83

But sin θ≈θfor small angles. Therefore

84

11.70: PROBLEM DEFINITION

Situation: The problem statement provides data describing aircraft takeoﬀand land-

ing.

Find:

(a) Landing speed.

(b) Stall speed.

SOLUTION

CLmax =1.40 which is the CLat stall. Thus, for stall

L/2

But

Therefore

85

11.71: PROBLEM DEFINITION

Situation:

An aircraft wing is described in the problem statement.

m=1000 kg

Area=S=16m2

wingspan = b=10m

V=50 m/s

Altitude = 3000 m

Find: Total drag on wing and power to overcome drag.

SOLUTION

Calculate pand then ρ:

Then

Then the total drag coeﬃcient

Total wing drag

86

11.72: PROBLEM DEFINITION

Situation: The problem statement provides data for a Gottingen 387-FB lifting vane.

Find:

(a) Speed at which cavitation begins.

(b) Lift per unit length on foil.

SOLUTION

Cavitation will start at point where Cpis minimum, or in this case, where

and for cavitation

87

Thus, ∆Cpavg. ≈1.45.Then

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11.73: PROBLEM DEFINITION

Situation: The distribution of Cpon the wing section in problem 11.72 (EFM10e) is

described in the problem statement.

Find: Range that CLwill fall within.

SOLUTION

89

11.74: PROBLEM DEFINITION

Situation: The drag coeﬃcient for a wing is described in the problem statement.

Find:DeriveanexpressionfortheCLthat corresponds to minimum CD/CLand the

corresponding CL/CD.

SOLUTION

90

11.75: PROBLEM DEFINITION

Situation:

A glider at elevation of 800 m descends to sea level

mass = 180 kg

S=20 m2

glideangeis1.7◦

ρ=1.2kg/m3

CL=0.83

Find: Time in minutes for the descent.

SOLUTION

Then

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11.76: PROBLEM DEFINITION

Situation: An aircraft wing is described in the problem statement.

Find: Drag force on the wing.

SOLUTION

Lift force

Thus

From Fig. 11.25 (EFM 10e) at CL=0.30,C

D≈0.06

Drag force

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11.77: PROBLEM DEFINITION

Situation: The problem statement describes an ultralight airplane.

Find:

(a) Angle of attack.

(b) Drag force on wing.

SOLUTION

Lift force

From Fig. 11.24 in EFM10e CD=0.06 and

93

11.78: PROBLEM DEFINITION

11.24 (EFM10e).

SOLUTION

There are several ways to address this design problem. One approach would be to

consider the wing area and velocities necessary to meet the power constraint. That

is,

Make plots of V0versus Swith CDas a parameter. Then use the constraint of the

lift equaling the weight.

2(0.00238 slugs/ft3)V2

Make plots of V0versus Swith CLas a parameter. Where these curves intersect

94