aero class #1

8/6/2019 Aero Class #1

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ASCI 309 Class #1

Aerodynamics concerns the interaction of the

atmosphere with moving bodies. This lies in

the realm of applied Physics - not only to

understand the dynamics of the moving body,

but also to understand the atmosphere

through which the body moves. So we will

start with a review of the applicable physicallaws. But first a quick look at a body of

interest.


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Physics Review - Dynamics

Newtons Laws

1st Law: Inertia. A body moves along a straight

path unless acted upon by an external force.

ex. skateboard vs. Mack truck

2nd Law: Acceleration. An unbalanced force acting

upon a body results in an acceleration. F = m a

ex. thrown baseball 3rd Law: Equilibrium. Forces occur in pairs.

ex. swimming


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Conservation Laws

Conservation of Energy: total=potential+kinetic=con.

potential=mgh, kinetic=mv2/2, total,2=total,1

ex. body in free fall with no air drag

Conservation of Linear Momentum: p=mv=con.

ex. billiard ball collision

Conservation of Angular Momentum: L=I=con.

ex. spinning ice skater


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Some definitions:

Work=Force acting over a distance: Wk=Fs

Power=Work/time

Pressure=Force/Area

Density=Mass/Volume

Speed of Sound=(RT) = a, (air)=1.4


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Recall from your first course in Physics where

bodies were considered to be point masses

and friction and rotational inertia were

ignored. We once again adopt simplifications

to make back-of-the-envelope calculations to

roughly estimate the flight path of airplanes.

Later we will make the calculations moredetailed to more closely approach reality.


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Treating an airplane as a point mass with the

four forces of Weight, Lift, Drag, and Thrust

acting upon it

is a simplification

but can lead to an

estimate of its flightpath under some assumptions such as

L = W = con. and D = T = con.

DT

W

L


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Starting with an initial altitude and initial

speed we can estimate a maximum altitude

the plane can reach using the initial kinetic

energy or the maximum speed the plane can

reach using the initial altitude - by utilizing the

conservation of energy principle.

For a given takeoff distance and takeoff speed,we can estimate the value of the constant

acceleration using the kinematic equations.


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Dimensions and Units

Every number we calculate represents some

physical quantity and thus has dimensions.

The fundamental dimensions are mass (m),

length (l), time (t), and Temperature (T). Other

quantities have derived dimensions which are

combinations of the fundamental dimensions,

e.g.: area (l2), volume (l3), density (m/l3).


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The dimensions all have units of measurement

attached to them. Usually either the

International system or the English system.

International system English system

mass (kilogram, kg) (slug)

length (meter, m) (foot, ft)

time (second, s) (second, s)

Temperature (Kelvin, K) (Rankine, R)


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In recent history there has been a move to

switch USA to the metric system as seen by all

the quarter mile tracks which are now 400 m

tracks, the metric bolts in automobiles and

motorcycles, and the kilometer highway

markers but alas we appear to be

permanently stuck with the English systemnow mixed with the metric system. Thus, we

will work problems in both systems.


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Force units are derived from Newtons 2nd LawF=ma, F(newtons, n), m(kg), a(m/s2) orF=ma, F(pounds, lb), m(slugs), a(ft/s2).

Similarly, weight, W=mg, g is the localacceleration due to gravity. Using metric units,W(n)=m(kg)g(m/s2) or W(lb)=m(slugs)g(ft/s2).

On and near the Earths surface, g=9.8 m/s2

org=32.2 ft/s2, depending on your choice ofunits.


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Pressure, p=Force/Area (n/m2) or (lbs/ft2)

Density, =Mass/Volume (kg/m3) or (slugs/ft3)

Temperature, T. While the Celsius andFahrenheit temperature scales are adequate

for weather forecasts and cooking,

aerothermodynamic calculations require the

use of absolute temperatures, Kelvin(K) or

Rankine(R).


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There are some other units still in common

usage that you should be aware of. If you go

to a horse race, the distances are in furlongs

where 1 furlong = 1/8 mile. If you are a sailor,distances are measured in nautical miles

where 1 nautical mile = 1 minute of arc on the

Earths longitude = 1.151 miles and speeds aremeasured in knots, 1 knot = 1 nautical mile/hr.

We too will find speeds given in knots.


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I came out of four years of undergraduate

engineering school with all of these

conversion factors indelibly burned into my

brain and lo and behold I discovered themetric system which was like a breath of fresh

air. The USA does a great disservice to science

and engineering by not adopting / mandatingthe usage of the metric system and once and

for all scrapping the English system.


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Derived Units

Velocity m/sec ft/sec

Work n-m (Joules) ft-lbs

Energy n-m (Joules) ft-lbs Power J/sec (watts) ft-lbs/sec

Pressure n/m2 lbs/ft2

Density kg/m3 slugs/ft3


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Conversions

2.54 cm / inch (exact), 0.3048 m / ft (exact)

1609 m / mi, 5280 ft / mi

1.151 mi / nautical mi, 1.151 mi/hr / knot 0.514 m/s / knot, 1.69 ft/s / knot

3600 sec / hr, 14.5 kg / slug

1 kg weighs 9.80 n = 2.20 lbs 1 slug weighs 32.2 lbs = 143 n

746 watts / HP, 550 ft-lbs/sec / HP


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Conversion Examples

An airplane is in level flight at 250 knots.

What is its speed in mi/hr? ft/sec? m/sec?

250 knots (1.151 mi/hr / knot) = 288 mi/hr

288 mi/hr(5280 ft/mi)(1 hr/3600 sec)=422 ft/s

250 knots (0.514 m/s / knot) = 128 m/s

An airplane weighs 16000 lbs. What is its massin slugs? kg? 16 000 lbs/32.2 ft/s2 = 497 slugs

497 slugs (14.5 kg/slug) = 7205 kg [W=mg]


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Problems 1 & 2

A airplane weighing 16000 lbs develops a

thrust resulting in a net force of 6000 lbs.

What is its acceleration down the runway?

An airplane is towing a glider. The tow rope is

20 below the horizontal and has a tension

force of 300 lbs exerted on it by the airplane.

Find the horizontal drag of the glider and theamount of lift that the rope is providing to the

glider. sin 20 = 0.342, cos 20 = 0.940


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Problems 3 & 4

The airplane in the first problem starts from

rest on the runway and takes off at 200 ft/s.

What is the elapsed time to reach takeoff

speed?

What is the takeoff roll for the airplane in the

preceding problem? (No wind)


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Problems 5 & 6

An airplane weighing 16000 lbs is in level flight

at 5000 ft and a ground speed of 200 ft/s.

What is its potential energy, its kinetic energy,

and its total energy?

If the preceding airplane went into a dive,

what would its altitude be when it reached a

speed of 400 ft/s? Assuming no change inthrust or drag and its energy is conserved.


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Physics Review - Gases

The periodic table lists the elements and theiratomic number (no. of protons in the nucleus)and their atomic mass (in atomic mass units

based on the no. of protons and avg. no. ofneutrons in the nucleus, 1 amu=1.66x10-27kg).

Gases may be monatomic (1 atom/molecule)or diatomic (2 atoms/molecule). Air, which isthe gas we are primarily concerned with, is78% N2, 21% O2, and a 1% mixture of others.


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Avogadro established the number ofmolecules in a mol of any substance to be6.02x1023. So air is (0.78x6.02x1023 molecules

of diatomic N + 0.21x6.02x1023

molecules ofdiatomic O + 0.01x6.02x1023 molecules of amixture of other gases)/mol.

The mass of each N2 molecule is2x14x1.66x10-27 kg and the mass of each O2molecule is 2x16x1.66x10-27 kg.


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So each mol of air has a mass of approx.0.0288 kg.

Gases are compressible and for low pressures

and high temperatures follow the perfect gaslaw (also known as the equation of state).pV=nRT, p=pressure, V=volume, n= no. mols,R = gas constant, T=absolute temperature. Wewill use a slightly different form: p=RT, R=gasconstant(air)=287 J/kg-K=1716 ft-lb/slug-R


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Atmosphere

Recall that the pressure at a depth h belowthe free surface of a liquid, p=p0 + gh, where:

p0=pressure at the free surface. Note that this

applies to a liquid which is incompressible. Airis compressible so the atmospheric pressure

as a function of altitude is a more complicated

calculation since both the temperature and

the density are functions of altitude. A

standard atmosphere model is chosen for

design calculations.


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Temperature vs. Altitude


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Atmosphere

Figure 3-4 (Anderson) is based on a standard

atmosphere. Since there are considerable

day-to-day variations in temperature,

pressure, and density, additional designcalculations are made based on worst-case

scenarios to insure reliability in extreme

conditions. Items for military use must alsopass survivability tests of salt spray, fungus,

dust/sand, and very high temperatures.


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Atmosphere

For reference, the sea level standard

conditions are:

pSL = 1.013x105 n/m2 = 2116 lbs/ft2

SL = 1.22 kg/m3 = 0.00238 slugs/ft3

TSL = 288 K = 519 R

Appendices A & B (Anderson) list the standard

atmosphere values of p, T, vs altitudeOther tables may also list the ratios: =p/pSL, =T/TSL

=/SL, note: =/


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Atmosphere

Just to further confuse things

There are six different altitude designations:

Absolute: ha

, meas. from the center of the Earth

Geometric: hG, meas. from sea level

Geopotential: h, assuming g=con.=g(sea level)

Pressure: using meas. p and std. atm. table

Temperature: using meas. T and std. atm. table

Density: using meas. p & T and std. atm. table


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Problems 7 & 8

Consider pb. 3.1, Anderson, p. 124. Hint: use

Fig. 3.4, eqn. 3.9, and eqn. 2.3.

Consider pb. 3.2, Anderson, p. 124.

aero class #1

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