## Chapter 1

## Theory Introduction

Chapter 1 Dole

The Bell X-1

First airplane to break the sound barrier

Modeled after a .50 caliber bullet because they were known to be stable at supersonic speeds

First flight Jan 25 1946

Broke the sound barrier Oct 14 1947

Mach 1.06

Powered by a rocket engine burning ethyl alcohol and oxygen

Put out about 6,000 lbs thrust

Empty weight 7,000 lbs

Max takeoff weight 12,250

Length 30’11”

Wingspan 28′

Height 10′

Wing area 130 sq ft

Max speed Mach 1.26

Range 5 minutes

Service ceiling 71,900′

Wing loading 94 lb/sq ft

Thrust to weight .49

Basic Physics terms and concepts

Aerodynamics – behavior of moving air and the forces it produces

means air in motion

The Greek we will speak

a alpha – angle of attack

d delta – static pressure ratio

? eta – prop efficiency

? theta – temperature ratio

? gamma – climb angle

? rho – air density

s sigma – density ratio

µ mu – coefficient of friction

The Basic units of measurements Page 12

Force – pounds

Distance – feet

Time – seconds

Velocity – ft/sec (fps)

Area – distance squared (ft2)

Pressure – force/unit area (lb/ft2)

Acceleration – change in velocity (ft/sec/sec) fps2

Useful Conversions

Force

Force is defined as push or pull changing the state of motion of a body

usually measured in pounds.

To calculate force you need 2 things

1. size of the force

2. direction of the force

F=ma

The 4 forces

1. Thrust force is force that moves the aircraft through the air

The force that must be generated to overcome drag

2. Weight – force that gravity causes on a mass

Mass is the measurement of the amount of material contained in a body

The same person may have the same mass but weigh less on the moon.

The 4 forces

3. Lift – component that is 90 degrees to the flight path and acts toward the top of the airplane

4. Drag – The component that is parallel to the flight path and acts toward the rear of the plane

3 and 4 he lumps together called Aerodynamic Force (picture)

Quantity

Scalar quantity – quantity that has size only; mass, time, and temp.

e.g. gas of 10 gallons

Quantity

Vector quantity – quantity that has both a size and direction; forces, accelerations and velocities

e.g. plane travels 50 miles north

Where does speed fit in?

Speed is scalar unless we consider the direction of the speed, then it is velocity

Vector addition vs Scalar addition

Scalar quantities can be solved by simple addition

You have 15 a side in your B-19

You add 5 gallons a side for a total of 20 gallons a side

Vector quantities are usually represented by arrows

3 vectors are represented

The aircraft vector

The wind vector

The drift angle or resultant vector

Magically we now have a right triangle and can use Pythagorean theorem to find the groundspeed and using the tangent, the drift angle

Vector Resolution

When replacing one vector with 2 or more

The resulting vectors are called component vectors and can be added vectorially to get the original vector

Moments

A moment has a turning or rotating effect through the plane’s cg.

It is a force applied by a moment arm

A moment is a force measured in ft-lbs or in-lbs

Pitching, rolling, yawing moments

Mathematically moments are classified as negative or positive

Arm

Is the shortest distance from the point of rotation to the line of action of the force.

Moment, Weight and Arm

Equilibrium

When there are no unbalanced forces or unbalanced mom

the sum of the forces = 0 and the sum of the mom = 0

Equilibrium

The airplane can be in equilibrium in a climb or descent

The airspeed must be constant and there must be no pitching, yawing or rolling moments.

A Few Definitions:

Inertia is the resistance of an object to a change in its state of motion.

Speed is the amount of distance that a moving object travels in a unit of time.

Velocity includes the speed of an object and the movement as well, A plane moving 120kts to the North

.

Newton’s Laws

1. A body at rest will remain at rest and a body in motion will remain in motion in a straight line, unless it is acted upon by and unbalance force.

Drag must be balanced by thrust

Lift and weight are equal in value in opposite directions.

Newton’s Laws

Acceleration/decceleration is a change in velocity measured in fps squared. You really don’t square anything that is just the unit for names sake.

Newton’s Laws

2. If an unbalanced force acts on a body, the body will accelerate in the direction of the force. And the acceleration will be directly proportional to the force and inversely proportional to the mass of the body.

Newton’s Laws

If a plane is traveling at 120kts north and a south wind of 20kts acts on the plane this is known as a positive acceleration.

If a plane is traveling at 120kts north and a north wind of 20kts acts on the plane this is known as negative acceleration or deceleration

Newton’s Laws

If a plane is traveling at 120kts north and an east wind of 20kts acts on the plane, the speed is not changed the acceleration is radial acceleration.

Newton’s Laws

Acceleration is directly proportional to the unbalanced force F.

a~F

The acceleration is inversely proportional to the mass of the object.

a ~ 1/m.

Newton’s Laws

The second law equation therefor is:

Newton’s Laws

3. For every action force there is an equal and opposite reaction force. (recoil of a gun)

Mass

Is a measure of the amount of material in a body.

Mass will not be effected by location. Mass is measured in slugs.

Weight = mass * acceleration of gravity

Weight

Is a force caused by the gravitational attraction of the earth, moon ect.

For the earth it is 32 fps2

For the moon it is about 6 fps2 (5.3 fps2)

So to figure slugs divide weight by 32

W=???? so…

Work

Work is when a component of force moves an object.

If you push against a wall and it doesn’t move no work is done until the wall moves.

Work = Force * distance

Energy is the ability to do work

Potential energy is the energy of position measured in ft-lbs.

A bomber carrying a 500 lb bomb at an altitude of 10,000 feet is an example.

PE=Weight * Height

PE = 10,000 * 500 = 5,000,000 ft-lbs

There is 5,000,000 ft-lbs of energy stored in the bomb.

Kinetic Energy

This requires the movement of an object

It is a function of mass and velocity

KE = 1/2mV2

As soon as the bomb is released it loses part of its potential energy. PE becomes less and less as the bomb falls reaching 0 at point of impact.

KE increases and reaches maximum at point of impact.

Total Energy = PE + KE

Energy can neither be created or destroyed but can change in form.

Power

Power is the rate of doing work

Power = work/time or force*dist/time

Horse power

(if speed is in fps)

if speed is kts thrust*V/325

Friction

Friction is the force that resists movement between surfaces that are in contact with each other.

Sliding, rolling and skin friction are all examples.

The squeezing force between the tires and the runway is called the normal force.

Friction

The constant that relates friction to the normal force is known as the coefficient of friction (a dimensionless number that is a constant called Mu µ).

The formula is F=µN where N is the force exerted perpendicular to the surface over which it slides.

The coefficient of friction Cf

A coefficient is a dimensionless number that is a constant for a certain set of conditions

For example, the Cf of a tire on concrete is about 1.0

Police forensics use a Cf of .7 in determination of skid marks vs speed

Wet concrete has a Cf about .3

Mu Values

- We use Mu values to give us an idea how slick the runway is:
- MU Value Braking Action

–0 through 6

–0 is bad

–6 is good

- 5-6 Good
- 4 Good to Medium
- 3 Medium (Braking is noticeably reduced)
- 2 Medium to Poor (Deceleration or directional control is medium to poor)
- 1 Poor (Braking and control significantly reduced)
- 0 Nil (Braking minimal to non-existent)
*EXAMPLE ATIS Report-*

“Runway*18,**MU**2, 3, 1**at**1825**Zulu, ice”.*