UNDERSTANDING AIRPLANE'S PERFORMANCE IN A PRACTICAL WAY

If you ask an engineer how to save fuel while flying an airplane he’s going to tell you: “Fly an angle of attack at least of  (Cd+(1.28a/S))/Cl“. However, if you show this equation to a pilot he won’t be able to understand most of it. Why does this happen? As Wolfang Langewiesche says in his book Stick and Rudder, engineers and pilots don’t speak the same language even though aviators fly the airplanes designed by engineers; and although the engineer needs to know exactly how the airplane fly based on equations, what a pilot needs more than the equations is a basic understanding of the principles of physics to apply these in a practical manner.

The objective of this article is to talk about some basic concepts and practical uses about Jet Performance that some airline pilots have misunderstandings about them. 

This doesn’t mean that pilots are not well prepared, this just mean that with all the information that has to be learned about the aircraft, regulation, weather theory, company policies, among other topics, these basic concepts start losing relevance. I believe that after reading this text, a pilot should feel more confident as well as start using this tools to make a flight more efficient by saving fuel and complying with ATC or company restriction in a better way.

The topics I’m going to talk about in this article are:

·       Power and Thrust

·       Max Angle of Climb

·       Max Rate of Climb

·       Best L/D Ratio

·       Max Endurance speed

·       Max Range speed

·       Long Range Cruise

POWER AND THRUST:

It is important to mention that when we talk about airplane performance, it is divided in two: Jet Performance and Reciprocating Engine Performance. This article will be centered in Jet Engines.

Usually we read about different type of speeds as best L/D ratio, long range cruise speed, max endurance speed, etc... As well, it is interesting that when we read about an airplane’s climb, we also read about different types of climbs as for example max angle of climb or max rate of climb. However, all these definitions have two concepts in common: Thrust and Power. These two although are related, they have different definition that sometimes people confuse, and they have extremely important implications defining the performance of an airplane. 

The turbojet engine is essentially a thrust-producing powerplant. This means that when we talk about thrust we talk about a force acting on an airplane. One of the main advantages of Jet engines is that the thrust it creates is almost constant and is relatively small affected by speed. On the other hand, when we talk about power, we’re talking the combination of available thrust and airspeed. This means that as the thrust of the jet engine is relatively constant with airspeed, power increases almost linear with speed.

In straight and level flight, thrust is the horizontal force that compensates Drag. When Thrust is higher than Drag, the airspeed is going to increase and when the opposite happens, the airspeed is going to decrease.

During a climb, there’s going to be a horizontal component of lift that will act opposite to thrust and the excess thrust is the one that will be responsible for the airplane to climb or if the opposite happens, to descend.

Having the definition of the force called thrust, what is power?

When we add speed and combine It with thrust, we get what is called power; it’s the combination between force, time, and distance. This means to use a force (Thrust), move it (distance), and move it fast (time), and this is what power means. In other words, apis to ply time and distance to the formula of Thrust.

So now, how do we relate these concepts in a practical way?

As we said before, in order to maximize the horizontal forces in an airplane in a positive way, we must increase thrust or decrease drag, in an equation this would look to maximize (T-D). In a level flight this would mean the airplane would have its maximum acceleration when we maximize the equation. However, to maximize power things are something different and needs a deeper analysis. As we saw in the figure above, thrust is almost constant and power increases linear with speed, so the faster the airplane is, the higher the power it creates. If you have this analysis you’re right but as we move faster, parasite drag increases so the power required to move the airplane increases too. As with thrust, the equation would look as maximizing (Pa-Pr) where Pa is power available and Pr is power required. How do we do this? Increasing the power available (Increasing speed or Thrust) or reducing the power required (reducing Drag). If we were flying at low speed, the excess drag would be due to induced drag but as we’re increasing speed, the drag that’s affecting as is parasite drag because induced drag has already decreased due to the increase in airspeed that creates a reduction in the angle of attack. If we find the correct speed that gives as enough power and reduces the parasite drag as much as possible, we’re going to be flying at a speed of maximum power.

Max Angle of Climb:

When we talk about maximum angle, we are referring to gain the maximum value on the y axis against the minimum increase in the x axis. In aviation words, this mean to gain the highest altitude in the shortest distance. In order to do this, we’ll have to Maximize the excess thrust (T-D). As we said before, the thrust in a jet engine is almost constant with speed, so in order to maximize the equation we stated before, we need to minimize the Total Drag. How can we minimize Drag? We minimize it when the parasite Drag and the Induced Drag are the same and this happens in a point called L/D Max.

Max Rate of Climb:

When we want to have the maximum rate of climb, in other words to increase altitude in the minimum time, we need to take into account the power available rather than the thrust available. As we said before, as we now need to climb fast and not in the shortest distance, time is critical now so we now talk about power. Which is our highest rate of climb? It is at the point where the excess power is at its maximum value.

Maximum Endurance Speed:

Endurance is the relationship between fuel and time. The main indicator we have of this in the airplane is the fuel flow indicator that is the relationship of the fuel used in a given time. If we are able to maximize this or to have the smallest fuel flow, we’ll be able to fly the airplane for the longest amount of time. As the book Aerodynamics for Naval Aviators says: "Usually this speed corresponds to 75% of the speed of Maximum Range."

As the fuel flow of the airplane is proportional to the thrust required, to have the smallest fuel flow we must have the lowest thrust required. In order to need a lower amount of thrust, we need to have a smaller amount of drag to be compensated. This is the same as to find the smallest amount of drag. We’ll have our Maximum Endurance Speed at our L/D Max speed, the speed of the smallest amount of thrust required.

 Maximum Range Speed:

Maximum Range Speed is defined as the speed that lets you fly the longest distance per given amount of fuel. While with max endurance we want to fly the longest possible time, with max range we don’t want to fly the longest time but we want to cover the longest distance. As it is said in the book Aerodynamic for Naval Aviators, “Maximum Range condition would occur where the proportion between velocity and thrust required is greatest”. The author also says “The maximum range is obtained at the aerodynamic condition which produces a maximum proportion between the square root of the lift coefficient (Cl) and the drag coefficient (Cd), or (.” What this definition looks like? The same as the definition where we find the maximum rate of climb. A point where we maximize lift and minimize drag with a specific speed. This speed is going to be higher than the maximum endurance speed.

As this can sound complicated, with a graph it’s going to be much easier to understand it:

With a particular weight, altitude, and configuration:

Maximum range is found at a speed where the increase of parasite drag is compensated with the increase of power of an engine. As you know, it is said that the drag increases as the square of the speed; but the power required increases as the cube of the speed. This means that we must find a point where parasite drag is increased but not so much. We find this drawing a line tangent to the curve of thrust required. The point where this line crosses the curve, is the optimum value for maximum range as shown in the graph above. What this graph also shows is that at max range speed the fuel flow will be higher than at max endurance speed but the range will be higher.

It is important to clarify that a lot of factor affect the maximum range condition as for example altitude, weight, and wind. As we are just focusing on the speed, we are assuming that these factors remain constant.

Practical use of the concepts mentioned above:

Until now we’ve talked only about the theory and we’ve clarified these concepts. Having said this, it is the moment to show how these can be really helpful for the pilots during a flight.

Obstacles clearance:

If you need to reach your MEA, GRID MORA, or any specific altitude due to obstacles or to deviate your route from bad weather what should be the appropriate speed? Max angle of climb speed would be the best speed for this situation because you’re going to reach the altitude you’re looking closer from your actual position for you to deviate from your actual route.

 ATC Request:

Usually in some congested airspaces with a lot of traffic, the ATC ask you to expedite or reach certain altitude as fast as possible. Which would be the suggested airspeed? The airspeed should be the best rate of climb because you’re going to reach that altitude faster than reducing to the best angle of climb airspeed. With the best rate of climb airspeed, you’re going to travel more distance but what the ATC wants you is to reach certain altitude as fast as possible to have the correct separation with other traffics. A constant mistake is that pilots reduce the airspeed to the best angle of climb because initially you’re going to have a vertical speed extremely high while you’re reducing airspeed due to the energy management theory but as soon as you reach the max angle of climb, you’re having the highest angle but there’s not a linear relationship between the angle and the rate of climb; the vertical speed you’d have at max angle of climb is going to be smaller than the one you’d have at a higher airspeed as the one you can get at the max rate of climb airspeed.

 Delays at the destination:

Delays are common and although some of these are predictable, some aren’t and with the fuel price as high as it is now, fuel optimization is a priority for airlines and in some flights the extra fuel you’ll have is going to be really small. In cases like this, is really helpful to use what we’ve said before. Usually ATC expects you to reduce your airspeed when you’re 3 minutes from the holding pattern but which speed should you maintain? There are maximum speeds depending on your altitude you must maintain but not a minimum. As in a holding you’re not concerned in covering a big amount of distance and what you need is to have fuel to be able to be as much time as possible in the holding pattern, the speed should be the L/D max speed in order to have the smallest fuel flow.

 Flying to the Alternate Airport:

In case you need to go to the alternate airport, which speed should you maintain? In this case you need to cover the maximum range as possible with the fuel remaining, so the max range airspeed must be the indicated one to use since the objective is to arrive to your alternate airport with the highest amount of fuel in case you need to use it there.

 Which are these speeds?

My flying experience has been mostly in Airbus aircraft so my answers are going to be based on Airbus philosophy definitions. However, with today’s technology, these speeds are the same in other aircraft and what only changes are the names.

Max angle of Climb or Max Endurance Speed is considered Green Dot. Max rate of climb or Max Range Speed is considered Cost Index 0. This last definition is interesting because Airbus manuals state that there is not a speed for Best rate of Climb so to have an approximately airspeed use the Severe Turbulence Airspeed. However, in the article published in the magazine Safety First by Airbus named Control your Speed in Cruise[3], it is said that Cost Index of 0 is the speed for max rate of climb.

 Long Range Cruise:

We have covered some specific speeds for specific situations, but what should be the normal speed in a flight?

If we fly slow we are going to be efficient in the way that we’re saving fuel. If we fly fast, we are going to be efficient because we’re saving time. What is more important? Depends on the airline needs. In the aeronautical industry, the parameter that includes this is called Cost Index. In a future article I’m going to talk about the benefits as well as the limitations of the Cost Index. However, the lowest the Cost Index is we’re going to be flying more to a fuel saving policy and the highest the Cost Index is we’re going to be flying in a lowest time policy.

Is there a linear negative relationship between fuel and time? The answer is no. You can try to increase the speed as much as you want in order to have more power available but due to the parasite drag increase which is not linear but exponential, the faster you fly the highest power you’re going to require so the more useless it’s going to be flying faster. You might reduce time but the excess of fuel consumption is going to be extremely high for the flight to be efficient. The point where the fuel consumption start increasing drastically is called Long Range Cruise Speed. This speed could be defined as another tangent line to the curve of the Total Drag. This should be the speed where in the absence of Cost Index all the airplanes should fly.

 BILIOGRAPHY 

Airbus SAS (January 2016). Control your speed during Cruise. Safety First.                                                                              

H.H Hurt, JR (1965). Aerodynamics for Naval Aviators. 

Wolfang Langewiesche (1994). Stick and Rudder.