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# Using graphs in Aeronautical Engineering

Outcomes

This unit of work addresses aspects of the following syllabus outcomes

The Student:

H1.2 differentiates between properties of materials and justifies the selection of materials, components and processes in engineering

H2.2 analyses and synthesises engineering applications in specific fields and reports on the importance of these to society.

Like to Fly one like this at Mach 3.2?

Movies, description and more pictures on http://www.dfrc.nasa.gov/Gallery/Movie/SR-71/index.html

Then you have to know how to read one of these:

SR – 71A Flight Envelope Diagram

The design of many items from an engineering point of view need to take into consideration the application of loads and forces (such as acceleration forces) and the reaction of the materials that the item is made from to these forces. Most of the analysis of the effect of forces and the consequent reaction to these forces is carried out using mathematical formulae. Often these formulae are very complex, or there may be a need to analyse the outcome of several formulae applying to a particular situation. Producing a graph representing the formulae allows the relationship between these formulae to be shown visually.

Graphs can therefore be used to solve problems relating to engineering mechanics, and they can be used to determine operating parameters set up by the interaction of a number of mechanical systems.

## Learn how to read Graphs.

The diagram above is very complex, so lets start with a light aircraft flight envelope

Flight Envelope Diagram

The diagram shows the load limits for this aircraft which the pilot must be familiar with to be able to fly the aircraft safely. Here they are, all in one place, on one graph.

The horizontal line at 0 on the graph represents the aircraft’s air speed. The unshaded section in the centre represents the flight conditions that should NOT be exceeded to ensure the aircraft structure is not overstressed.

### Where does it all come from?

It starts with this graph, the result of experimental testing on engineering materials;

Stress Strain diagram courtesy of Industrial Heating

This is a Stress – Strain diagram which is used by engineers to interpret material strength. To obtain this type of graph it is necessary to carry out a tensile test on a ductile material such as a piece of mild steel. A test piece of known dimensions is placed in the testing machine known as a Tensometer. To determine its strength, a load is applied to “stretch” the test piece. The size of the load is measured and the stress induced in the piece is calculated by dividing the applied load by the cross sectional area of the test piece. The calculated value – stress - is represented on the vertical axis of the graph.

As the load increases the material “stretches”, it elongates. The elongation is measured and converted to strain by dividing the change in length by the original length of the test piece. The calculated value - strain - is represented on the horizontal axis of the graph.

Following the green line on the graph starting at 0: As the stress increases, the material stretches. Initially it is “elastic”. That is, if the load is removed the test piece will return to its original length. This occurs until the material reaches its “proportional limit” shown on the graph as point A. This part of the graph (O to A) is a straight line. This deformation is called “elastic deformation” and the ratio of stress to strain is a constant known as “ Young’s Modulus”.

Between A and B on the graph many materials show a definite ‘yield point’ and this is often used as a basis for design calculations. For materials without a definite yield point (many brittle materials) an offset method is used to calculate a ‘theoretical’ yield which is used for design calculations. The offset yield is often calculated for 0.01% strain (X on this graph).

As we follow the green line from A to D, the material continues to stretch, but the elongation is now permanent. This is called “plastic deformation”, and if the load is removed the material will NOT return to its original length.

Point D on the graph represents the material’s greatest ability to support a load. It is termed the “Ultimate tensile stress” (UTS) and is the figure quoted when we compare the strengths of different materials. Once the UTS has been reached the cross sectional area of the test piece reduces (a process known as necking) and the applied load drops accordingly. Failure occurs at the end of the green line at X.

When aircraft are designed the size of the parts is determined by the loads those parts have to withstand. Other factors such as the cyclic nature of the loads is also considered.

Depending on the design process being applied a ‘factor of safety’ can be applied to either the ‘UTS’ or the ‘yield strength’ to provide a ‘maximum allowable stress’ from which the minimum safe size of components can be calculated.

### Back to the Flight envelope diagram

The axes of this graph show the load factor (vertical) and indicated air speed (horizontal). The coloured areas represent certain limits for other flight parameters such as structural failure, and calm air flight.

Using this type of graph enables to pilot to quickly ascertain whether conditions require a change in flight functions to ensure safe flight conditions. A large amount of data can be analysed without the need for mathematical formulae, calculators or data books.

The border between the red and yellow sections on the flight envelope diagram is the point where 100% load limit is reached for the aircraft!

But why the rest of the Flight envelope diagram?

Activity 1:
Go to http://www.grc.nasa.gov/WWW/K-12/airplane/vel.html and use the simulator to determine the effect of airspeed on lift. When you double the airspeed, what happens to lift.

Activity 2:
Go to http://www.grc.nasa.gov/WWW/K-12/airplane/incline.html and use the simulator to determine the effect of angle of attack on lift. When you increase the angle of attack, what happens to lift.

Activity 3:
Go to http://www.grc.nasa.gov/WWW/K-12/airplane/factord.html Briefely state the effect of angle of attack on induced drag. When you increase the angle of attack, what happens to induced drag.

Activity 4:
Go to http://www.grc.nasa.gov/WWW/K-12//airplane/atmosi.html and use the simulator to determine the effect of altitude and combined factors on lift. When you increase the altitude, what happens to lift.

The green shaded area on the Flight Envelope Diagram is an area where the aircraft may be flown in calm air. Engineers calculate the additional loads that may be experienced due to wind gusts and turbulence. If an aircraft is flown at speeds below the green zone on the graph, and it flies into a wind gust, the additional forces caused by the gust (a sudden increase in airspeed) should not cause the aircraft to exceed its load limit.

The yellow shaded area on the Flight Envelope Diagram provides a margin of safety so that the aircraft’s structure is not jeopardized in the event of an unexpected event.

You will note that there is a possible negative load permissible on the aircraft. Negative loads are sometimes applied during maneuvers. The aircraft for which this diagram was drawn would not be able to do aerobatics. An aerobatic aircraft would necessarily allow negative loads similar to the positive ones. The aerobatic limits to this aircraft would be described in the flight manual.

Further explanation: http://www.faatest.com/books/FLT/Chapter17/VgDiagram.htm

We’re ready to start interpreting the Blackbird Diagram

On the left of the graph is a small section terminating at .....................Feet

Blank to be 25,000

The note on this area states “Normal speed range for take off and landing only”

The abbreviation KEAS stands for Knots equivalent airspeed - the Ground equivalent airspeed measured in Knots. 145 Knots is approx 268Kph, 250 Knots is approx 463Kph.

Activity 5:
What happens during take off and landing that would change the flight characteristics of the aircraft such that different maximum speeds would be specified?

Activity 6:
Why does the minimum air speed increase from 300 to 310KEAS?

Activity 7:
The pilot is flying the aircraft at 73,000 feet and wishes to bank the aircraft to turn. He is traveling at the maximum airspeed. What must he do before turning.