Prepare for your exams
Get points
Guidelines and tips

Prepare for your exams

Study with the several resources on Docsity

Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips

Sell on Docsity

Log in Sign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search Store documents

The best documents sold by students who completed their studies

Search through all study resources

Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents

20 Points

For each uploaded document

Answer questions

5 Points

For each given answer (max 1 per day)

All the ways to get free points

Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

University Rankings

Discover the best universities in your country according to Docsity users

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

From our blog

Exams and Study

Go to the blog

Lab 1: Flight Power Relations - Lecture Notes, Exercises of Aeronautical Engineering

Bidhan Chandra Krishi Viswavidyalaya Aeronautical Engineering

Lecture notes on the topic of flight power relations. It covers the generation of thrust during flight, the drag power, and the contribution of different components to the total drag. The document also discusses the relationship between flight power and duration in an electric aircraft, and the importance of parameter coupling and design optimization.

Typology: Exercises

2011/2012

Uploaded on 07/22/2012

sehgal_98 🇮🇳

4.8

(4)

137 documents

1 / 4

This page cannot be seen from the preview

Don't miss anything!

!

Flight Power Relations 9 Feb 06

Lab 1 Lecture Notes

Nomenclature

c

C

D aircraft drag

L aircraft lift

W aircraft weight

T propeller thrust

V ﬂight speed

S reference area (wing area)

b wing span

AR wing aspect ratio

L lift coeﬃcient

D drag coeﬃcient

CDA0 drag area of non-wing components

ℓ wing-airfoil proﬁle lift coeﬃcient

d wing-airfoil proﬁle drag coeﬃcient

ρ air density t

E

Ω

T

η

P

P thrust power ( ≡ TV )

shaft motor shaft power

elec electric power (Volts × Amps)

m electric motor eﬃciency

p overall propeller eﬃciency

ideal ideal propeller eﬃciency

R propeller radius

c thrust coeﬃcient

m motor rotation rate

Ω propeller rotation rate

λ prop eller a dvance ratio

Re chord Reynolds number

elec electrical (battery) energy

max maximum ﬂight duration

Thrust Power

Generation of thrust during ﬂight requires the expenditure of power. In steady level ﬂight,

T = D, and hence the thrust power is equal to the drag power.

P ≡ T V = DV (steady level ﬂight) (1)

In steady level ﬂight we also have W = L, which gives the velocity in terms of other relevant

parameters.

1

W = L = ρV 2 S CL (2)

2

!

1/2

2W

V = (3)

ρ S CL

The drag power can then be given as follows.

1

DV = ρV 3 S CD (4)

2

C

2W31/2

D

DV = (5)

3/2

ρ S CL

We will assume that the typical wing airfoil sees the same local cℓ as the overall aircraft CL,

so we can employ 2D airf oil cd(cℓ, Re) data.

cℓ = CL (6)

The aircraft drag coeﬃcient can now be broken down into three basic components.

CC2

D = CDA0 + cd(CL, Re) + L (7)

S π AR

1

docsity.com

Partial preview of the text

Download Lab 1: Flight Power Relations - Lecture Notes and more Exercises Aeronautical Engineering in PDF only on Docsity!

( )

Flight Power Relations 9 Feb 06

Lab 1 Lecture Notes

Nomenclature

c

C

D aircraft drag L aircraft lift W aircraft weight T propeller thrust V flight speed S reference area (wing area) b wing span AR wing aspect ratio L lift coefficient D drag coefficient CDA 0 drag area of non-wing components ℓ wing-airfoil profile lift coefficient d wing-airfoil profile drag coefficient ρ air density t

E

T

η

P

P thrust power ( ≡ T V ) shaft motor shaft power elec electric power (Volts^ ×^ Amps) m electric motor efficiency p overall propeller efficiency ideal ideal propeller efficiency R propeller radius c thrust coefficient m motor rotation rate Ω propeller rotation rate λ propeller advance ratio Re chord Reynolds number elec electrical (battery) energy max maximum flight duration

Thrust Power Generation of thrust during flight requires the expenditure of power. In steady level flight, T = D, and hence the thrust power is equal to the drag power.

P ≡ T V = DV (steady level flight) (1)

In steady level flight we also have W = L, which gives the velocity in terms of other relevant parameters.

1 W = L = ρV 2 S CL (2) 2 ( ) 1 / 2 2 W V = (3) ρ S CL

The drag power can then be given as follows. 1 DV = ρV 3 S CD (4) 2 2 W 3 C 1 / 2 DV = D (5) ρ S (^) C^3 /^2 L We will assume that the typical wing airfoil sees the same local cℓ as the overall aircraft CL, so we can employ 2D airfoil cd(cℓ, Re) data.

cℓ = CL (6)

The aircraft drag coefficient can now be broken down into three basic components.

C

C 2

D =^

CDA 0

cd(CL, Re) + L^ (7) S π AR

1

The last term is the induced drag, which directly depends on the aspect ratio of the wing. This is defined in terms of the wing span and area.

b^2 AR = (8) S

Figure 1 shows the three CD components versus CL for a typical 1.5 m span light RC sport aircraft.

CL

1.4 CDAo/S^ cd^ CDi^ CD

0.0 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0. CD Figure 1: Drag polar and drag polar components for electric sport aircraft. AR = 9. 0

For a typical operating point at CL = 1.0 (low speed) and CL = 0.3 (high speed), indicated by the symbols in Figure 1, the three components contribute roughly the following percentages to the total drag:

CL

CDA 0 /S

cd

37 % 52 %

C^2

L/π^ AR

45 % 9 %

CD

The corresponding flight power is shown in Figure 2.

Flight Power and Duration

In an electric aircraft, the flight power is provided by an electric motor, driving a propeller with some efficiency ηp.

P = ηp Pshaft (9)

The motor itself has efficiency ηm, and is supplied by a battery which outputs electrical power Pelec.

Pshaft = ηm Pelec (10) P = ηp ηm Pelec (11)

Con: Reduces V , which increases Tc, which decreases ηideal, which decreases ηp
Use more efficient motor, with larger ηm.
Pro: Direct 1/ηm reduction of Pelec
Con: More efficient motor may be heavier, and hence may increase W.

Other Pros and Cons may be present in addition to those listed above, depending on the situation.

Much of the activity which occurs during aircraft design and sizing consists of identifying and quantifying such couplings. Knowing the couplings then allows suitable tradeoffs to be performed, in order to find the best set of design parameters to maximize the design objective. Once a good or optimum design has been reached, all its competing tradeoffs are in balance, so that there are no more “easy” design changes which can be made without adversely affecting something else.

Lab 1: Flight Power Relations - Lecture Notes, Exercises of Aeronautical Engineering

Related documents

Partial preview of the text

Download Lab 1: Flight Power Relations - Lecture Notes and more Exercises Aeronautical Engineering in PDF only on Docsity!

Flight Power Relations 9 Feb 06

Lab 1 Lecture Notes

C

C

E

T

P

P

C

C 2

D =^

CDA 0

CDA 0 /S

C^2

CD