Sae Formulas

Use of the formula

Formula

Source of the Formula

Planform area of the wing (S)

1 2

Root cho

croot =

rd of the wing

Mean aerodynamic chord of the wing

c

ρ v 2 C l

b(1 + λ )

3(1 + λ )

Reynolds nm!er

MQP FINAL

2 S

2(1 + λ + λ 2 )

=

MQP nal

L

S =

Re =

MQP FINAL

c root

MQP FINAL

ρ vc µ

WING AND TAIL

WING AND TAIL

WING

AERODYNAMIC

AERODYNAMIC

AND TAIL

PROPERTIES

PROPERTIES

AERODYN AMIC PROPERTI ES

Lft coe!ce"t

C Lα

MQP FINAL

2Π ( AR)

= 2+ 4+

( AR) 2 β 2

η 2

(1 +

tan 2 Λ

= 1 − M 2

β 2 η =

β 2 MQP FINAL

C l α ( 2Π / β )

F = 1.07(1 + d / b) 2 "here Mach nm!er

Aerodynamic center of the wing

M =

x ac c

v

MQP FINAL

R (TEMP ) γ

=−

∂C M , LE ∂C N

MQP FINAL

Normal force coe#cient

= C l cos α + C d sin α

C n

Qarter chord moments

C m, LE

PROPULSION

C n

= C m,c / 4 −

MQP FINAL

MQP FINAL

4

PROPULSION

PROPULSI ON

Power ot$t

P = I ⋅ V

MQP FINAL

R%P%M

RPM = K v ⋅ V battery

MQP FINAL

&'ations for diameter of the $ro$eller

PERFORMANCE

T =

MQP FINAL

P V pitc T

A prop

=

! prop

= 2⋅

0.5 ⋅ ρ ⋅ V e

2

A prop

Π

PERFORMANCE

PERFORM ANCE

AL *RA+ Indced drag

!total = !ind$ced , "in# + !0

1

C dra# =

+ ! feateredprop

(C l ) 2

MQP FINAL MQP FINAL

Π ( AR)e e = 1.78(1 − 0.045( AR) 0.68 ) − 0.64

Parasite drag

Form factor of the wing

FF c %c S "et ,c

f ,c

C d 0 Laminar and tr!lent s,in friction coe#cients

∑ C

C f ,lam

=

C f ,t$rb

=

=

MQP FINAL

c

S ref MQP FINAL

1.328 Re 0.455 (log 10 Re)

2.58

+ (1 + 0.144 M 2

4  0.6  t  t    FF = 1 +   + 100  [1.34 M 0  ( x / c ) m  c   c  

MQP FINAL

Form factor of the em$ennage

1

f =

Feathered $ro$ drag

MQP FINAL

 60 f   FF = 1 + 3 +  400 f    4  A   max  Π 

C d 0, feat eredprop

= 0 .1

nblade&

Aprop

Π ( AR) blade

S ref

MQP FINAL

AIRCRAFT

AIRCRAFT

AIRCRAFT

STA#ILITY AND

STA#ILITY AND

STA#ILIT

CONTROL

CONTROL

Y AND CONTROL

Primary e'ations to calclate netral $oint Sta!ility en.elo$e

x np

=

S '

C Lα , " xac, "

+ η '

C Lα ,"

+ η '

S S ' S

− 0.15 + xac," + η ' x nf

=

C Lα , '

d α ' d α d α '

MQP FINAL MQP re$ort

d α

S ' C Lα , ' d S C Lα , "

S ' C Lα , ' d α '

1 + η '

SE = xnp

C Lα , '

S C Lα , " d α

− xmf

/inge moments

' Total = ' Aerodynam ic + ' (ei#t = C m ,in#e( 0.5

MQP FINAL

STRUCTURAL

STRUCTURAL

STRUCTU

ANALYSIS

ANALYSIS

RAL ANALYSIS

LIF P&R 0NI SPAN A /& R F /& "IN+

∫ L 2

0

!ending moment as a fnction of s$an wise (y) $osition1 and fond the moment at the wing root area moment of inertia

0

 2 y  dy = ( 1−   2  b  2

v

M ( y )

= − M root + ∫ &L

1 0

0

I ))

MQP FINAL

2

b

= I )) , &*$a re − I )) ,circle =

 2 &  1 −   d&  b  4 l &id e

12

4 − Π r ole

4

MQP FINAL

MQP FINAL

Ma2imm !ending stress

M root ( l &id e / 2)

=

σ max

MQP FINAL

I ))

UA$

UA$

UA$

LONGITUDINAL

LONGITUDINAL

LONGITU

STATIC STA#ILITY

STATIC STA#ILITY

DINAL

AND CONTROL

AND CONTROL

STATIC STA#ILIT Y AND CONTROL

CONTRI#UTION OF AIRCRAFT COMPONENTS TO STA#ILITY

0A3 "IN+S 4NRI50IN

C m 0 "

= C m

C mα

= C L

"

ac "

α "

0A3 F0S&LA+& 4NRI50IN

=

C m 0 f

=

C mα f 0A3 AIL 4NRI50IN

 + +  + C L 0  c# − ac  c   c   + +  +  c# − ac  c   c  "

− , 1

, 2

36.5S c 1

l f

∫ " (α )dx 2 f

0 "+ i f

0

x =l f

∑" 36.5S c

2 f

x = 0

∂ε $ ∆ x ∂α

C m 0t

= η V ' C L ( ε 0 + i" − it )

C mα t

d ε  = −η V ' C L  1 −   d α 

α t

α t

ε = ε 0 ε =

+

d ε d α

2C L"

Π AR"

α "

M*&LLIN+ AN* SIM0LAIN F A 0/ 0A3 *6NAMI4S M*&LLIN+ AN* SIM0LAIN F A 0/ 0A3 *6NAMI4S M*&LLIN+ AN* SIM0LAIN F A 0/ 0A3 *6NAMI4S

&'ation for netral $oint

+ NP c

=

+ ac c

−

C mα f C Lα

"

d ε  + η V '  1 −   d α 

M*&LLIN+ AN* SIM0LAIN F A 0/ 0A3 *6NAMI4S

UA$ DIRECTIONAL

UA$ DIRECTIONAL

UA$

STA#ILITY

STA#ILITY

DIRECTIO NAL STA#ILIT Y M*&LLIN+ AN* SIM0LAIN F A 0/ 0A3 *6NAMI4S

UA$ COMPONENTS CONTRI#UTION

F0S&LA+& 3&RI4AL AIL "IN+ 4NRI50IN 6A"IN+ MM&N 4&FFI4I&N *0&  SI*&SLIP F /& 0A3

C nβ f

= −, n , Rl

C nβ

= C L

v free

C nβ

"

C nβ 0A3 MM&NS F IN&RIA MI a!ot o2 a2is MI a!ot oy a2is MI a!ot o7 a2is Prodct of inertia a!ot o2 oy a2es Prodct of inertia a!ot o2 o7 a2es Prodct of inertia a!ot o7 oy a2es AERODYNAMIC FORCES AND DERI$ATI$ES

=

S " b

η v α

S v xv &

v

S b

C L2

4Π AR = C nβ + C nβ f

"

+ C n

= ∑ δ m( y 2 + ) 2 ) 2 2 I y = ∑ δ m( x + ) ) I ) = ∑ δ m( y 2 + x 2 ) I xy = ∑ δ mxy I x) = ∑ δ mxy I y) = ∑ δ my) I x


S f& l f

β v



Longitdinal deri.ati.es + $

+ $ - $

- $

= − ρ S.C ! = − ρ S.C L

+ "

1 2 M = ρ . S c C m 2 ∂C m 1 M $ = ρ . 2 S c 2 ∂.

- "

+ "

M M $

- " *ownwash deri.ati.es

4ontrol deri.ati.es

 − ∂C !   2 ∂α   ∂C 1  = ρ .S   L + C !  2  ∂α  =

1

ρ .S  C L

∂C ∂ + 1 ∂ + 1 = = ρ .S ! ∂" . ∂α  2 ∂α  ∂C ∂ - 1 ∂ - 1 = = ρ .S L - " = ∂" . ∂α  2 ∂α  ∂C ∂ M 1 ∂ M 1 = = ρ .S c m M " = ∂" . ∂α  2 ∂α  + "

=

∂ +

+ η = - η =

∂η ∂ -

=

M η =

1 2 1

=

∂η

M η =

ail .olme coe#cients


∂ M

2

ρ . 2 S

=

∂η ∂ M ∂η

ρ . 2 S

1 2

=−

∂C ! ∂η

∂C L ∂η

ρ . 2 S c 1 2



∂C m ∂η

ρ . 2 S c V a ′2

V T

=

S T l T

V F

=

S F l F

S c S b


Normal force deri.ati.es

- $ = −

ρ v0 S

( M C 0

L

+ 2C L

M 2m ρ S c (C - α  ) - " = 4m ρ v S - " = − 0 ( C Lα + C ! ) 2m ρ V 0 S c - * = C - * m

(

- " = Pitching moment deri.ati.es

ρ V 02 S

M *

LA&RAL *&RI3AI3&S

= =

M δ

=

Lv

=

Lv L p Lr Lδ

= = = =


)

(C ) - δ

2m

M "

)

ρ V 0 S c

C mα

2 I y

ρ V 0 S c 2 4 I y

ρ V 02 S c

C mδ

2 I y

ρ V 0 Sb 2 I x

C l β

ρ V 02 Sb 2 I x

C l β

ρ V 0 Sb 2 4 I x

ρ V 0 Sb 2 4 I x

ρ V 02 Sb 2 I x

C m*


C lp C l r

C l δ


6A"IN+ MM&N *&RI3AI3&S

N v


ρ V 0 Sb C nβ 2 I )

=

ρ V 02 Sb N β = C nβ 2 I ) ρ V 0 Sb 2 N p = C np 4 I ) ρ V 0 Sb 2 N r = C nr 4 I ) ρ V 02 Sb N δ = C nδ 2 I ) Lateral force deri.ati.es

/ v / v

ρ V 0 S

=

2m


C yβ

ρ V 02 S

=

C yβ 2m ρ V 0 Sb / p = C yp 4m ρ V 0 Sb / r = C yr 4m / δ 0A3 LN+I0*INAL MIN Assming stic, 2ed Fre'ency *am$ing ratio

ω n&p

2m

- α M *

=

$0 M *

ζ &p &stimating 0A3 $hogoid Fre'ency *am$ing ratio

=

ρ V 02 S

ω n

p

=

C yδ

− M α

+ M α  +

=−

- α $0


2ω n &p M*&LLIN+ AN* SIM0LAIN F A 0/ 0A3 *6NAMI4S

− - $ # $0

− + $

ζ p

=

λ 1, 2

= −ζ pω np ± iω n

2ω np 1 − ζ 2

Sae Formulas

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