## Mechanics Tutorial 8 - Drag, Lift and Friction

 Contents

This aeroplane is flying at a constant speed at a constant height There are two pairs of opposing forces:

• Weight due to gravity opposed by the lift from the wings;

• Thrust from the engine opposed by the drag from the air.

If the lift is equal to the weight, the aeroplane will stay at a constant height.  If the thrust is equal to the drag, the speed will be constant.

Drag

Drag is a result of collisions of air molecules on the body of the aeroplane.  The faster the aeroplane flies, the more frequent the collisions are, and the greater the change of momentum.  We will see later that change in momentum results in force.

You can feel drag for yourself by pedalling fast on a bicycle.  When you are travelling slowly, there is little air resistance.  The faster you go, the greater the air resistance becomes.  And that means you have to work harder.

 How can drag be reduced?

Air is a fluid, which is a material that can adopt the shape of a container.  In other words a fluid is any liquid or gas.

Drag depends on these factors:

• The cross-sectional area facing the direction of movement;

• The density of the fluid;

• The square of the speed;

• The drag coefficient.

The formula (which is not on the syllabus) is this: The drag coefficient (CD) depends on the shape of the object and a factor called the Reynolds number.  You can see it’s getting complicated…  The diagram below shows the way shape affects the drag.

 Shape and Form Form Drag / % Skin Friction / % 0 100 10 90 90 10 100 0

You can see that a long thin shape has very low drag, but high skin friction.  However the skin friction is less significant in causing drag than the cross-sectional area.  So it’s a good idea to make fast aeroplanes have a long cylindrical shape.  This eight-oared racing shell is long and thin.  It has a low form drag, but a high skin friction. Fluid Flow and Aeroplanes

An old saw in the aviation world is that "if it looks good, it flies good as well". Source not known

This aeroplane, Concorde, was a supersonic commercial transport aircraft that was designed in the nineteen-sixties.  Even now it looks sleek and modern.  However it shared more in common with the Vulcan bomber (a large bomber introduced in the nineteen fifties) than with today’s aircraft.  Its load was limited and it required a lot of fuel.  Flying it was not easy either.  The skin friction was considerable at very high speeds; its skin temperature could reach about 80 oC.

Concorde was retired in the early twenty-hundreds after a disastrous accident to one of the planes. A fuel tank on the left hand side was struck by an object that had fallen on the runway.  The fuel tanks were chock-full (which they should not have been) and the shock of the strike split the tank open, so that it was gushing out 100 litres a second.  This led to a serious fire.   The aeroplane was overloaded and and could only just fly.  Then the engineer shut down the engines on the left, resulting in the machine becoming un-flyable.

All the remaining Concordes are now in museums. Vulcan to the Skies

This is XH558, a Vulcan bomber that continued to fly until September 2015.  Like the Concorde, the remaining Vulcan bombers have now become valuable museum pieces.

This is a utility aircraft. Wiki Media Commons

The Shorts Skyvan is neither elegant nor fast but can carry a large load.  It is also very easy to fly.

Aeroplane design is about making compromises.  Skinny long cylindrical aircraft may be fast, but they don’t carry much.  Stubby aeroplanes like the one above can carry good loads but are not fast.

Lift

The collision of molecules on surfaces in the right place gives rise to lift.  Wings on aircraft are specially designed to use the Bernoulli effect.  Air moves fast around the top of the wing and more slowly around the bottom.  This causes a pressure difference. From GCSE you will know that:

Pressure (N m-2) = force (N) ÷ area (m2) So if we know the pressure difference and the wing area, we can easily work out the lift.

Atmospheric pressure is measured in bar (b).

1 bar = 1000 mb = 1.013 × 105 N m-2

 Calculate the pressure exerted on the wings of a light aircraft of mass 1100 kg if the wings have an area of 16 m2.  How does this compare with atmospheric pressure which is 1.013 × 105 Pa?

Lift can be increased by increasing the angle of the wing, or by altering the shape of the wing by lowering a flap.  Aircraft coming in to land have their flaps lowered:

• It increases the lift at low speeds;

• It also increases the drag, helping to slow the plane down. Aircraft taking off need to rotate, which means that they are at an angle to the ground.  This gives a higher angle of attack, leading to more lift.  Pilots call this alpha because the angle is shown as a in diagrams However, if the angle of attack is too high, or the speed is too low, the airflow breaks up, leading to a stall.  The plane will no longer fly and falls.  At height, this can be easily recovered (and is a standard exercise with novice pilots).  Near the ground it can be disastrous. Source not known.  If this is your image and you want it removed or acknowledged, please tell me.

In flight, the faster the aeroplane, the more the lift.  This could make the aeroplane go higher, so to keep to the same level the pilot puts the nose down by adjusting the trim.  This is done through trim tabs on the elevators.

Is drag ever useful?

Yes it is.  Large aircraft use spoilers to help to slow them down.  These are sizeable panels that stick out into the airflow and increase drag considerably. Wiki Media Commons

 How has the pilot increased the drag on this plane?

Aeroplanes with high landing speeds have problems slowing down with brakes alone.  So a braking parachute can be deployed to slow the aeroplane down effectively.

 Use your understanding of kinetic energy to explain why. Wiki Media Commons

However this has to be repacked before the aeroplane takes off again.  In the plane above, you can also see the spoiler sticking up above the cockpit.

Power is the rate of doing work.   We have seen how power can be related to speed:

Power (W) = force (N) × speed (m s-1)

P = Fv

We also saw how drag force was related to speed: By considering the two relationships above, suggest how the power is related to the speed in an aircraft.

Consider this light aircraft: Wiki Media Commons

It is driven by a 1.4 litre petrol engine which gives out about 100 PS (75 kW).  It flies at about 200 km h-1.

 Use your answer to question 5 to work out the power that would be needed to make this aircraft fly at 400 km h-1.

If the aircraft above were to be made to fly at 400 km h-1, the forces acting on it would be so high that it would probably break up.  All aircraft have a never exceed speed, known to pilots as VNE.

The physics of aviation is discussed in detail in aeronautical engineering.  It can be quite complex.  Aircraft design is a compromise.  Very manoeuvrable aircraft are difficult to fly as they are unstable.  Utility aircraft such as the Shorts Skyvan are not very manoeuvrable (they don’t have to be), and are easy to fly.

Frictional Forces

Friction is a force that opposes the relative movement of solid surfaces and fluid layers.  We mostly associate it with the force that opposes the movement of solid surfaces, but there are a number of different types of friction:

• Dry friction – the force opposing relative movement of solid surfaces;

• Fluid friction – the friction between layers of a fluid;

• Lubricated friction – the friction of a layer of lubricant between two solid layers;

• Skin friction – the friction that occurs on the interface between a solid and a fluid;

•  Internal friction – the friction between layers of atoms in a solid that enables it to resist deformation. Drag and friction are terms that are often used interchangeably.  However it is incorrect to label drag as friction, although there is the component of skin friction that contributes to drag.   Remember to write friction, or you will be writing fiction.

Dry Friction

If you look at what appears to be a smooth surface under the microscope, you will see that the surface is not at all smooth, but looks more like a mountain range. So it doesn’t take a genius to so that we have to do a job of work to make these two surfaces slide over each other.  This wastes energy, which is why engines that have a lot of surfaces that move relative to each other are rather inefficient.

Dry friction can be reduced somewhat by separating the layers of solid metal by a layer of a liquid such as lubricating oil. Lubrication does not get rid of friction completely.  It reduces it.  There is friction due to the lubricant itself, which is a viscous fluid.

When two surfaces are rubbing against each other, there is energy lost, which is turned into heat.  If there is no lubrication, the surfaces can get so hot that they expand and increase the friction even more.  In an extreme case, the surfaces can fuse together.  An engine in which this happens is described as seized up, and the damage is expensive. Lubrication systems ensure that lubricant (almost always a mineral oil) gets to all moving parts.  The lubrication system also ensures that the bearings are kept cool as well as lubricated.  In some engines, there is an oil cooler, either with the main cooling system of the engine, or with the air.

Coefficient of Friction

The friction between two flat surfaces can be measured quite easily and quantified in the coefficient of friction.  Consider a block moving on a flat horizontal surface: In this case the normal force is equal (and opposite) to the weight.  The coefficient of friction can be worked out using: The term m is “mu”, a Greek letter ‘m’, which is the Physics code for coefficient of friction.  It has no units.

 A piece of metal is moved on a wooden surface with a pulling force of 12.6 N. Its mass is 2.45 kg. What is the coefficient of friction?

If we put the block on a slope at an angle q, the weight is no longer the normal force.  The normal force is one of two perpendicular forces of which the weight is the resultant.  So we will need to work out the normal force. From previous work, we know that: Since: We can write: It doesn’t take a genius to see that weight cancels out to give us: Since: We can write: This result tells us:

• That the weight of an object on a slope does not affect the maximum angle to which a object can be raised to before it slides down the slope;

• The maximum angle is solely determined by the coefficient of friction.

 Worked Example A slope has an angle of 25o.  What is the coefficient of friction of the surface if an object just remains stationary on the slope? Answer m = tan 25 = 0.466 (no units)

What we have studied above is called static friction.  It is the force needed to make the two surfaces move.  Kinetic friction is the friction between moving surfaces.  The two are different.  The difference is discussed in the next section.

Here are some figures for static friction:

 Material 1 Material 2 Coefficient of Static Friction Aluminium Steel 0.61 Cast iron Copper 1.05 Water ice Water ice 0.05 PTFE PTFE 0.04 Glass Glass 0.90 Wood Wood 0.25 – 0.50 Rubber Tarmac 0.9

It is possible to have a coefficient of friction greater than 1.0.  It’s not usual, but it simply means that the force we have to apply to get an object moving is greater than its weight.  Silicone rubber against silicone rubber can have a coefficient of friction of about 1.15.

Kinetic Friction (Pre - U and IB only)

If you push a heavy box across a floor, you will notice that it takes more force to get it going.  Once it is moving, the force needed is slightly less.  When you do an experiment to measure the coefficient of friction, you will find that the force needed to make the object slide along the surface is rather less than the force needed to shift the object.

The coefficient of friction for a stationary object is for static friction.  Its physics code is ms ("mu-ess").  The force that will just move a static object is given the code Fs.   We know from above that:

Fs = msN

The force required to keep the object moving at a constant speed against the friction is called the kinetic force (or dynamic force).  It has the physics code Fk.  The coefficient of friction in this case is the coefficient of kinetic friction, with the code mk.  The equation is similar:

Fk = mkN

Here are the figures for both static and dynamic friction:

 Material 1 Material 2 Coefficient of Static Friction Coefficient of Kinetic Friction Aluminium Steel 0.61 0.47 Cast iron Copper 1.05 0.29 Water ice Water ice 0.05 0.02 PTFE PTFE 0.04 0.04 Glass Glass 0.90 0.40 Wood Wood 0.25 – 0.50 0.20 Rubber Tarmac 0.9 0.50

Notice how the kinetic friction is less than the static friction.

 Worked Example A block of copper of weight 12 N is at rest on a perfectly level and smooth cast iron surface. (a)  Calculate the force that will just make the block move. (b) The same force is applied when the object starts to move.  Calculate the acceleration of the object. (Take the value of g as 9.8 N m-2.) Answer (a)  Use: Fs = msN     Fs = 1.05 × 12 N = 12.6 N (= 13 N to 2 s.f.)   (b)  We need to work out the kinetic force:  Fk = mkN        Fk = 0.29 × 12 N = 3.48 N        Difference between the static and kinetic force = 12.6 N - 2.48 N = 9.12 N        We now need to know the mass:           m = 12 N ÷ 9.8 m s-2 = 1.22 kg        Now use Newton II:          a = F/m = 9.12 N ÷ 1.22 kg = 7.4 m s-1 (to 2 s.f)

In many cases friction is essential.  The rubber feet of my laptop keep it firmly on the table as I type this stuff out.  If you want to check out the usefulness of friction, try walking down an icy pavement in leather-soled shoes.  You will quickly find the answer.

If rubber didn’t have the high coefficient of friction, our cars would skid much more easily.  With rubber, the high coefficient of friction can be explained by the idea of mechanical keying. The pliable surface of rubber is pushed into the road, increasing the area of contact.  The diagram shows how the grip is improved.

 A weight of 6.9 N is on a slope. When the normal force is measured, it is 6.0 N, and the object is just about to slide down the slope. a. Calculate the angle of the slope; b. Calculate the coefficient of friction between the material of the object and the material of the slope.