On Minimum Energy, and Maximum Rate, Aircraft Turns
150305 JLG
This document consists of two parts: in the first part gravity is neglected, whereas in the second
it is included.
Minimum Energy Turn, Gravity Neglected
Disregarding gravity, and banking 90 d
Drag of Circular Cylinder
Joachim L. Grenestedt
January 21, 2007
Assume that we mount a circular cylinder perpendicular to the flow in a wind tunnel and
measure drag at various wind speeds. The diameter of the cylinder is d=0.1 m. Reynold's
number is
Re
Forces and moments on wing with elliptic pressure distribution
Joachim L. Grenestedt
2009-01-30
Assume that the force per unit length in the spanwise direction fulfills the (elliptic)
equation
q
q
o
2
2
y
1
l
q q o 1
y
l
2
where l is half the span
Climb, Propeller and Jet Aircraft
Joachim L. Grenestedt
2011-02-15
Equilibrium of an aircraft during steady climb requires
L mg cos 0
(1)
T D mg sin 0
where L is lift, T is thrust (which is parallel to the direction of flight), D is drag and mg is
weight.
Predicted Climb and Ceiling, VariEze
Equilibrium of an aircraft during steady climb requires
L mg cos 0
T D mg sin 0
where L is lift, T is thrust (which is parallel to the direction of flight), D is drag and mg is
weight. Drag is
D D0 Di f 0 q
L2
b 2eq
w
Gliders, best glide ratio and minimum sink
Joachim L. Grenestedt
2011-02-15
Let a glider be gliding downwards with an angle relative to the horizon. Equilibrium of
the aircraft during steady gliding requires (see Fig. 1)
L mg cos 0
D mg sin 0
where L is l
Induced Drag
Joachim L. Grenestedt
January 24, 2005
Induced drag, or drag due to lift, can be calculated using some different approaches, such
as Prandtl's lifting line theory or a momentum based approach. We will presently use the
latter. Assume that an
Yang Shangdong MECH328
HW#1
1. Answer these through the interview:
a. To what airport did you go?
Queen City Airport
b. Who did you interview?
Carl Wilson
c. What airplane does he/she own and/or fly?
d. What is the power of its engine?
PA-32 Piper Lance
3
8.1.
CD
C7Dmiu
OLmux
ACLmX
CHAPTER 8
HIGH-LIFT DEVICES
Symbols.
drag coefcient
minimum lift coefcient
maximum lift coefcient
increment of maximum lift coefficient
normal-force coefcient
ap normal-force coefcient based on the area of the ap
volumeow coef
Wing spar analysis
Joachim L. Grenestedt
March 17, 2014
Abstract
A wing spar consisting of top and bottom flanges that carry the bending moment, and a web that
carries transverse shear, is analyzed and designed.
Wing Spar Shear and Bending Moment
Assuming
CAFE Design Studies
Joachim L. Grenestedt
080206
CAFE Score
The CAFE score is
Overall score = velocity^1.3 x MGP x payload^0.6
The drag will be assumed to be
D D0 Di f 0 q
m2 g 2
b 2 qe
The power to propel the aircraft is
P Dv
and the engine power is
Pe
Aerodynamic Center
Joachim L. Grenestedt
March 11, 2004
Study a wing with a cross section as shown in Fig. 1. The lift L and moment M1/4 around
the quarter point of the wing section are
dL qcl cdy qcl 0 cdy
dM 1 / 4 qc m c 2 dy
where q=v2/2 is the dynamic
Wing aspect ratio
J.L.Grenestedt
2012-04-09
The intention of this study is to give an indication of what aspect ratio is reasonable for a
dynamically soaring aircraft. Major simplifications are naturally made.
Assume that the aircraft has the mass m, maxi
Stability and Equilibrium
ROUGH DRAFT
Joachim L. Grenestedt
February 18, 2008
Start by studying a flying wing with a symmetric profile as shown in Fig. 1. We know
that the lift is L approximately
L qS
2
2
(1)
where q=v2/2 is dynamic pressure, is air densi
Range and Endurance
Joachim L. Grenestedt
April 11, 2013
Range for Propeller Driven Aircraft
For propeller driven aircraft with reciprocating engines, the specific fuel consumption c
may be assumed to be independent of flight velocity. Thus
1 dm
P dt
c
o
Propeller Actuator Disk Theory
Joachim L. Grenestedt
January 27, 2005
Study an airplane in steady flight at speed v0. It may be easiest to consider the plane
stationary in a wind tunnel with the free stream velocity v0. Let the speed of the air in the
pro
Aerodynamic Forces
Joachim L. Grenestedt
March 29, 2005
According to Max Munk's formulas for airships, there is no force due to yaw on the
fuselage. However, there is a destabilizing moment,
M 2q V
where q v 2 / 2 is the dynamic pressure, is the side slip
Atmosphere
Joachim L. Grenestedt
January 18, 2005
The radius of the Earth is approximately 6370 km. Space is generally defined as the
region outside 100 km above sea level. The atmosphere is thus relatively thin compared
to the radius of the Earth. Approx