The four main forces acting on an aircraft in flight are:
Ideally, aircraft should be designed in such a way that the following reactions occur automatically:
Each of the four main forces has its own point of action. Lift acts through the centre of pressure, and weight acts through the centre of gravity. Thrust and drag act in opposition to one another, parallel to the direction of flight, through points that vary with aircraft attitude and design. We assume that the thrust force from the engine–propeller combination is acting in the direction of flight, although this is not always the case. For instance, at a high angle of attack (AoA) and slow speed, the aircraft has a high nose attitude, with the propeller shaft inclined upwards to the horizontal direction of flight. Therefore, assuming that thrust acts in the direction of flight simplifies the discussion, and it is easy to say that in straight and level flight:
LIFT = WEIGHT and THRUST = DRAG
The LIFT/WEIGHT forces are greater than the THRUST/DRAG forces by approximately 10 to 1.
The aircraft needs to be longitudinally stable. Longitudinal stability is in the pitching plane about the lateral axis, whereas lateral stability is about the longitudinal axis. To be longitudinally stable, an aircraft has to be stable about the lateral axis. The pitching moments of thrust and drag must equal the pitching moments of lift and weight. If an aircraft is disturbed in the lateral plane, it must have the ability to return to the original attitude without pilot input.
For reference, we have the lift formula below:
From the formula, we can see that for straight and level flight, lift must equal weight. If the speed of the aircraft is decreased, the lift coefficient must be increased (i.e., angle of attack increased) to keep the lift force equal to weight. If our forward speed is increased, the coefficient of lift must be decreased (i.e., angle of attack decreased) to maintain level flight and retain lift equal to weight. To obtain the required lift at low speed, a high AoA is required, while at high speed, only a small AoA is required. Since we are considering level flight, the pilot sees the angle as an aircraft pitch attitude relative to the horizon: NOSE-UP AT LOW SPEED and FAIRLY NOSE-LEVEL AT HIGH SPEED.
The centre of pressure (C of P) and centre of gravity (C of G) vary in position—the CP changing with angle of attack and the CG with fuel burn off and passenger or cargo movement. The result is that the lift–weight combination sets up a COUPLE, which will cause a nose-down or a nose-up pitching moment, depending on whether the CP acts behind or in front of the CG. Similarly, the effect of the THRUST–DRAG couple depends on whether the thrust line is below the drag line (as is usually the case) or vice versa. The usual design is to put the CP behind the CG, so that the L–W couple is nose-down, and the thrust line lower than the drag line, so that the T–D couple is nose-up. Any loss of power will weaken the nose-up couple and, consequently, the nose-down lift–weight couple will pitch the aircraft into a descent, thereby maintaining flying speed—a fairly safe arrangement. The lift–weight couple and the thrust–drag couple should balance each other in straight and level flight so that there is no residual moment acting to pitch the aircraft either nose-up or nose-down. The ideal situation rarely exists between the four main forces and so the horizontal stabiliser/elevator is required to compensate for differences between LIFT/WEIGHT and THRUST/DRAG pitching moments. A problem arises, however, if the THRUST/DRAG positions are reversed, e.g., in a flying boat. If the thrust line is above the drag line, application of power will produce a nose-down couple—a decidedly unwanted reaction as both couples LIFT/WEIGHT and THRUST/DRAG produce a nose-down moment. The solution is the tail plane is inclined at an appropriate angle of incidence that will produce a nose-up pitching moment when power is applied. If a steady pressure needs to be exerted on the control column so that the elevator produces the required balancing force, then this is a clear indication that the aircraft needs to be trimmed to relieve the load.
The effect of weight on level flight: In normal flight, the weight gradually reduces as fuel is burned off. If an aircraft is to fly level, the lift produced must gradually decrease as the weight reduces. For example, if there is a sudden decrease in weight, say by a dozen skydivers jumping out, then to maintain straight and level flight, the lift must be reduced by a corresponding amount. This is achieved by either decreasing the coefficient of lift, by reducing the angle of attack, or by reducing the airspeed so that less lift is produced.
Performance in straight and level flight: If an aircraft is to be operated in the most efficient manner, then it should be flown at the best L/D ratio AoA (about 4°). Any alteration of this angle will lead to a reduction in efficiency. For example, as the weight reduces due to fuel burn off, thrust needs to be reduced to lower the lift produced so that it continues to equal the weight. If the power is kept constant with the weight decrease, then the lift must be decreased by reducing the AoA. This will result in some loss of efficiency.
Remember: POWER + ATTITUDE = PERFORMANCE
Here we are introducing the power available and power required graph for an aircraft to maintain level flight. The graph below plots the power required to maintain level flight and the power available to overcome level flight at a range of speeds. Remember that this graph only represents one aircraft at straight and level flight, at one altitude, weight, and power setting. The power required to move an aircraft through the air at a constant speed can be expressed as a formula:
Minimum speed for level flight: Is a low, high-drag speed requiring a lot of power to overcome level flight. Minimum speed does not necessarily coincide with the stall speed.
Maximum speed for level flight: As above, although this time, the high-drag condition is mainly due to parasite effects.
Best rate of climb, VY: Occurs where the most power is at our disposal to climb the aircraft.
Best endurance: Is the minimum power setting. At this speed, we require the least power to maintain level flight and, as such, the lowest fuel burn.
Best range speed: Is a little higher than the best endurance speed. The best range speed gives us the least fuel burn for maximum speed. No other point on the graph gives us such a good ratio of these two factors. It is, therefore, the best range speed, and found at the tangent to the curve.
Effect of altitude on climbing: The power of an aircraft engine decreases with altitude. Even if it is possible to prolong sea-level pressure to greater altitude by boosting (supercharging), the power will inevitably decline when the aircraft reaches a height at which the boosting method employed can no longer maintain the set power. Note that the power required to fly at minimum speed is increased at altitude. This effect is caused by the fact that although the minimum drag speed in terms of IAS remains the same at all heights, the speed used in the calculation of thrust power is the TAS, which increases with altitude for a given IAS. The thrust power required to fly at any desired IAS thus increases with altitude. The range of speeds between minimum and maximum level flight speed is reduced at altitude, and the best rate of climb speed is also reduced. The absolute ceiling, a height where the rate of climb is reduced to zero, is the point where both curves become tangential to each other. The service ceiling is where a small amount of residual excess power is left, to provide for a rate of climb of no more than 100 ft/min. The above is shown on the power required vs. power available graph below.
Effect of weight: For an aircraft in level flight, for a given airspeed, if the weight is increased, in order to maintain level flight, the angle of attack will need to be increased. This increased angle of attack results in increased drag, meaning increased power required to maintain straight and level (Power Required = Drag × TAS). The result on the power required curve is that it is moved up and slightly to the right to indicate an increased minimum speed, increased stall speed, and lower maximum speed.
Thrust is the force produced by the propeller. An aircraft propeller generates thrust by accelerating a mass of air towards the rear. The amount of thrust generated depends on the increase in velocity given to the mass of air entering the propeller disc—the greatest increase in velocity occurs when the aircraft is stationary. As airspeed is increased, the propeller is less able to cause further acceleration to the air entering the disc, and thus the thrust decreases. Eventually, a high speed is reached where the propeller is unable to accelerate the air passing through it, and no thrust will be produced.
The thrust required for straight and level flight is equal to the amount of drag produced in straight and level flight. Hence, the thrust required curve is commonly referred to as the drag curve.
Power is the rate of doing work. It is measured by the combination of the force applied and the velocity that it produces. The power required curve combines the thrust required for level flight with the TAS gained. The power available curve gives an indication of how capable the engine–propeller combination is in effectively applying thrust at different true airspeeds. Although the ‘raw’ thrust available from the propeller decreases with speed, when combined with the TAS to obtain power available, a slight increase with speed is shown. Power is the measure of how effectively that thrust can be put to work, e.g., to fly the aircraft level or to climb at different true airspeeds. Note the difference between the thrust and power curves is that the maximum thrust is available when the aircraft has zero forward speed and decreases as airspeed is gained. The power available, on the other hand, increases as airspeed is gained. Let’s compare the two curves.
The graph shows thrust required (drag) curve situated on top, with the power required curve on the bottom. Points to note:
When the difference in power available compared to power required (excess power) is derived from the above curves, we can see a similar picture. Notice that we can now plot VX on this curve.
It would be equally as valid to write ‘rate of climb’ instead of ‘excess power’ above. The two are proportional.
Discuss the following questions in class now.