Blade Component Theory

Prof. Dr . Mustafa Cavcar

Anadolu University, School of Municipal Aviation

Eskisehir, Turkey

[email protected] edu. tr

The simple energy theory provides an initial thought regarding the functionality of a propeller but not sufficient information intended for the detailed design. In depth information can be acquired through evaluation of the makes acting on a blade aspect like it is actually a wing section. The makes acting on a small section of the blade happen to be determined after which integrated above the propeller radius in order to predict the pushed, torque and power attributes of the propeller.

R

П‰

c

ur

dr

dT

w

Ve

VR

Sixth is v

dL

О±i

ОІ

О±

П†

dF

П‰r

dD

Figure 1 . Propeller knife element with velocity and force plan.

В© Prof. Dr . Mustafa Cavcar, 2004.

1

A differential cutter element of blend c and width doctor, located at a radius r from the propeller axis, is demonstrated in Figure 1 . The element is shown behaving under the influence of the rotational velocity, П‰r, forwards velocity of the airplane, V, and the induced velocity, t. Vector sum of these velocities produce Empieza = П‰ r & V + w

(1)

The section has a geometric pitch perspective of their zero lift line of ОІ. If it is assumed that V and П‰r are known, then computation of the activated velocity watts is desired to find О± i, and therefore the section angle of attack О±. Knowing О±, and the section type, C l and C g can be determined, then the differential box lift and drag in the section follows. However , w depends on dL which in turn is determined by w. Thus the problem is tightly related to the finite wing problem but is more complicated because of the helicoidal geometry with the propeller [1]. Merged Momentum вЂ“ Blade Factor Theory

A starting estimated value of w can be acquired by putting on the energy theory rules to an annulus of width dr and radius l (Figure 2). In this case

dT = ПЃdA(V + watts cos П† )2w cos П†

(2)

dr

l

R

Number 2 . Annulus to compute w.

In Eq. (2) w cos П† is applied while the induced velocity instead of w alone, because only w cos П† component of the induced speed acts in the axial way as shown in Determine 3. In case it is assumed that О± my spouse and i is small , w may differ only with the radius, then simply

В© Prof. Dr . Mustafa Cavcar, 2004.

2

watts = VRО± i

(3)

Therefore , the differential thrust applied to the annulus becomes dT sama dengan ПЃ (2ПЂrdr )(V & О± iVR cos П† )2О± iVR cos П†

(4)

V

w

П†

wcosП†

П†

rotation

planes

VR way

Figure three or more. Axial circulation component of the induced speed.

Since the powerful angle of attack with the section can be

О± sama dengan ОІ в€’ П† в€’О±i

(5)

then simply, the differential lift working on B rotor blades will be

dL = M

ПЃ

2

Ve2 a 0 ( ОІ в€’ П† в€’ О± my spouse and i )cdr

(6)

where a zero is the lift up curve incline of propeller's blade section. The assumptive value of a0 is definitely 2ПЂ, yet experiment shows that the value to get a two-dimensional airfoil is typically regarding 5. several per radian, or about 0. you per degree.

The thrust and the gigantic force acting on the cutter element

dT = dL cos(П† + О± we ) в€’ dD sin(П† + О± i )

dF sama dengan dL sin(П† + О± i ) + dD cos(П† & О± we )

(7)

(8)

However , if it is thought that Ve в‰… VR, and the move is much smaller than lift, after that:

dT = dL cos П†

or perhaps

В© Prof. Dr . Mustafa Cavcar, 2005.

3

dT = W

ПЃ

VR2 ca zero ( ОІ в€’ П† в€’ О± i ) cos П†dr

2

(9)

From Eqs. (4) and (9)

пЈ« О» Пѓa 0V L

+ a couple of

пЈ by 8 x VT

О± i2 + О± i actually пЈ¬

пЈ¬

пЈ¶ Пѓa 0V L

пЈ· в€’ 2 (ОІ в€’ П† ) sama dengan 0

пЈ· 8x V

T

пЈё

(10)

exactly where

x=

l

V

Bc

О»

, О»=

, VT sama dengan П‰R, Versus R = О»2 + x a couple of VT, Пѓ =

, П† = bronze в€’1

L

x

П‰R

ПЂR

The induced position of attack О± i could be extracted from (3) because пЈ®

you пЈЇ пЈ« О» Пѓa 0V L

О±i sama dengan в€’ пЈ¬ + a couple of

2 пЈЇ пЈ¬ back button 8 by VT

пЈ° пЈ

пЈ¶

пЈ·+

пЈ·

пЈё

пЈ« О» Пѓa 0V 3rd there’s r

пЈ¬ + 2

пЈ¬ x 8x V

To

пЈ

two

пЈ¶ Пѓa 0V Ur ( ОІ в€’ П† ) пЈ№

пЈє

пЈ· +

пЈ·

пЈє

two x 2VT

пЈё

пЈ»

(11)

If the propeller geometry defined simply by blade pitch ОІ, cutting tool chord span c, and the ratio from the forward speed to the idea speed О», are given, the induced angle of assault can be...

Recommendations: [1]

McCormick, B. W., Aerodynamics of V/STOL Airline flight, Academic Press,

Orlando, 1967.

В© Prof. Dr . Mustafa Cavcar, 2004.

5