Project-1: Powertrain for aircraft in runways

Part A:

1. Search and list out the total weight of various types of aircrafts.

STUDY 1:

The aircraft gross weight (also known as the all-up weight and abbreviated AUW) is the total aircraft weight at any moment during the flight or ground operation.

An aircraft's gross weight will decrease during a flight due to fuel and oil consumption. An aircraft's gross weight may also vary during a flight due to payload dropping .

At the moment of releasing its brakes, the gross weight of an aircraft is equal to its takeoff weight. During flight, an aircraft's gross weight is referred to as the en-route weight or in-flight weight.

Weight of Various Types of Aircraft Weight :

1.Glider

Glider is a fixed wing plane that is supported in flight by the dynamic reaction of the air against its lifting surfaces, and whose free weight does not depend on an engine. Most gliders do not have an engine, although motor glider have small engines for extending their flight when necessary by sustaining the altitude (normally a sailplane is on a continuously descending slope) with some being powerful enough to take off self launch.

Weight of Glider planes : 110 kg - 200 kg

2.Powered Lift

A powered lift aircraft takes off vertically under engine power but uses a fixed wing for horizontal flight. These aircraft do not need a long runway to take off and land, like helicopters , but they have a speed and performance similar to standard fixed wing aircraft in combat or other situations.

Weight : 160 kgs

3.Fighter Aircraft

A fighter aircraft, often referred to simply as a fighter, is a military fixed wing aircraft designed primarily for air to air combat against other aircraft. The key performance features of a fighter include not only its firepower but also its high speed and maneuverability relative to the target aircraft.

Weight : 13500 kgs

4.Transport Planes :

Military transport aircraft or military cargo aircraft are used to airlift troops, weapons and other military equipment to support military operations. Transport aircraft can be used for both strategic and tactical missions, and are often diverted to civil emergency relief missions.

Weight : 250,000 kgs

5.Aerobatic Planes

An aerobatic aircraft is an aerodyne (a heavier-than-air aircraft) used in aerobatics, both for flight exhibitions and aerobatic competitions.

Weight : 771 kgs

2.Is there any difference between ground speed and air speed?

STUDY 2:

Ground Speed	Air speed
Ground speed is the airplane’s speed relative to the surface of the Earth	Airspeed is the speed relative to the air it is flying in.
Ground speed is what determines how fast an aircraft will get to its destination	Airspeed is what determines whether there is enough airflow around an aircraft to make it fly
Ground speed is simply the sum of airspeed and wind speed.	It is independent of ground speed.

• The above two diagram relative velocity with respect to aircraft reference and ground reference.
• Here wind speed is the vector difference between ground and air speed. On a perfect still day the wind speed is zero and it is equal to the ground speed.
• If the measured air speed is greater than the observed ground speed the wind speed becomes positive.

3.Why is it not recommended to use aircraft engine power to move it on the ground at Airport?

STUDY 3:

Towing is coupling two or more objects together so that they may be pulled by a designated power source or sources. The towing source may be a motorized land vehicle, vessel, animal, or human, and the load being anything that can be pulled

Although many aircraft are capable of moving themselves backwards on the ground using reverse thrust (a procedure referred to as a powerpack), the resulting jet prop might cause damage to the terminal building or equipment. Engines close to the ground may also blow sand and debris forward and then suck them into the engine, causing damage to the engine. A pushback is therefore the preferred method to move the aircraft away from the gate.

Although most aircraft are capable of moving themselves backwards on the ground using reverse thrust, a procedure called as a powerpack, it is not typically done due to the following reasons:

• The jet blast from the engines can damage the terminal building and nearby equipment. It can even throw away people standing nearby.
• Engines can blow sand and debris.
• Engines can suck in sand and debris which can cause serious damage to the engine.
• It is easier for the truck driver to see the surroundings better than the pilot sitting in the cockpit with limited windows.
• The pushback truck driver knows the airport better than the pilot.
• The plane engines are very loud. This noise can add up substantially when multiple planes are moving around the airport. It won't be a pleasant experience for people sitting inside the terminal, as most people don't even like the sound of powerful motor-bikes.
• It saves fuel. Virgin Atlantic had proposed a new system in which the pushback trucks will push the plane all the way to the runway to save fuel and reduce impact on nearby environment.

Taxiing is the movement of an aircraft on the ground, under its own power, in contrast to towing or push-back where the aircraft is moved by a tug. The aircraft usually moves on wheels, but the term also includes aircraft with skis or floats (for water-based travel).

The power for taxiing comes from the engines itself. If it is a propeller powered aircraft, the propeller provides thrust and pulls the aircraft, like it would in air. If it is a jet engine, the exhaust air that comes out of the engine creates a forward force due to Newton's third law and moves the airplane.

Airliners have nose wheel steering, controlled by a cockpit control called a tiller. The tiller allows nose wheel to rotate at quite extreme angles making tighter turns possible. It also reduces the fuel consumption as you do not need much engine power during taxiing. If rudders were used, the power has to be increased to make sure sufficient air flows over the rudder surface to make it effective.

Once on the take off roll and the airplane gains sufficient speed i.e. enough air flows over the rudders, pilots go back to using the rudder pedals to maintain the center line.

Some large airplanes with multi wheel main gears have a tendency to scrub the Tyres on the tarmac when nose wheel is steered. To counter this problem, an automatic main gear steering is inbuilt in the aircraft. This makes the main gears turn the opposite direction to that of the nose wheel, greatly decreasing the wear on the Tyres.

Small general aviation aircraft uses the rudder for turns during taxi. They don't have a separate control for nose wheel. In such airplanes, to make tighter turns, you could use differential braking. That is, if you want to make a tight turn for example to the left, you would push the upper part of your left rudder pedal which would apply left braking. This allows the airplane to make a sharper turn to the left.

4.How an aircraft is pushed to runway when its ready to take off?

STUDY 4:

In aviation, pushback is an airport procedure during which an aircraft is pushed backward away from its parking position, usually at an airport gate by an external power. Pushbacks are carried out by special, low-profile vehicles called pushback tractors or tugs.

Although many aircraft are capable of moving themselves backward on the ground using reverse thrust (a procedure referred to as a powerback), the resulting jet blast or prop wash would cause increased noise, damage to the terminal building or equipment, and hurt airport staff due to high-speed debris. This debris would also be sucked into the engine, as it is in normal use, and cause excessive wear - a major cause of wear on aircraft engines is during ground use. A pushback is therefore the preferred method when ground-handling aircraft.

Pushbacks at busy aerodromes are usually subject to ground control clearance to facilitate ground movement on taxiways. Once clearance is obtained, the pilot will communicate with the tractor driver (or a ground handler walking alongside the aircraft in some cases) to start the pushback. To communicate, a headset may be connected near the nose gear.

Since the pilots cannot see what is behind the aircraft, steering is done by the pushback tractor driver and not by the pilots. Depending on the aircraft type and airline procedure, a bypass pin may be temporarily installed into the nose gear to disconnect it from the aircraft's normal steering mechanism.

Once the pushback is completed, the towbar is disconnected, and any bypass pin is removed. The ground handler will show the bypass pin to the pilots to make it clear that it has been removed. The pushback is then complete, and the aircraft can taxi forward under its own power.

5.Learn about take off power, Tyre design, rolling resistance, Tyre pressure, brake forces when landing.

STUDY 5:

a. Take off power:

Take off performance can be predicted using a simple measure of the acceleration of the aircraft along the runway based on force equilibrium.

The forces involved will be,

T – Thrust of propulsion system pushing aircraft along runway.

D – Aerodynamic Drag of vehicle resisting the aircraft motion.

F – Rolling resistance friction due to the contact of wheels or skids on the ground.

During take-off run the imbalance in these forces will produce an acceleration along the runway.

dv/dt = T - D - F /m

The procedure for take-off will be that the vehicle will accelerate until it reaches a safe initial flying speed. The pilot can then rotate the vehicle to an attitude to produce climb lift and it will ascend from the ground. The determination of this safe flying speed or rotation speed, V_R, is a critical factor in determining take-off performance.

For safety reasons V_R is usually determined as being 1.1 × V_STALL

V_{STALL :} is the lowest speed that the aircraft can be flown before the airflow starts to separate from wings as the angle of attack becomes too great. The wing is assumed in this case to be in take-off configuration or "clean".

It can be calculated based on knowledge of the aircraft take-off configuration and hence the maximum achievable lift coefficient C_L(max). As shown in the previous section , to maintain level flight the lift produced must equal the weight, hence the stall speed can be calculated as,

b. Tyre Design of aircrafts:

When it comes to safety, Tyres are one of the most important components of aircraft. They help to absorb the shock of landing and provide cushioning. It also provides the necessary traction for braking and stopping of an aircraft.

An aircraft Tyre is designed to withstand extremely heavy loads while landing, take off, taxing and parking. The number of wheels required for aircraft increases with the weight of the aircraft, as the weight of the Aeroplan needs to be distributed more evenly.

Carcass plies are used to form the tire. They are sometimes called casing plies. An aircraft Tyre is constructed for the purpose it serves.

Unlike an automobile or truck Tyre, it does not have to carry a load for a long period of continuous operation. However, an aircraft Tyre absorbs the high impact loads of landing and also it’s operating at high speeds for a short time when required.

Retreading – Retreading is methods of restoring a worn Tyre by renewing the tread area or by renewing the tread area plus one or both sidewalls. Repairs are included in the Tyre retreading process.

Load Rating – Load rating is the maximum permissible load at a specified inflation pressure.

Ply Rating – Ply Rating is used to identify the maximum recommended load rating and inflation pressure for a specified Tyre. It is an index of Tyre strength.

Speed Rating – The speed rating is the maximum takeoff speed to which the Tyre has been tested.

Skid Depth – Skid depth is the distance between the tread surface and the deepest groove as measured in the Mould.

Aircraft Tyres must have an approved speed and load rating and have sufficient clearance when retracted through landing gear to allow for Tyre growth. Tyre growth is the increase in the size of the Tyre due to centrifugal forces at high speed.

c. Rolling Resistance:

Rolling resistance, sometimes called rolling friction or rolling drag, is the force resisting the motion when a body (such as a ball, tire, or wheel) rolls on a surface. It is mainly caused by effects; Thonon elastic at is, not all the energy needed for deformation (or movement) of the wheel, roadbed, etc., is recovered when the pressure is removed. Two forms of this are hysteresis losses , and permanent plastic deformation of the object or the surface (e.g. soil). Another cause of rolling resistance lies in the slippage between the wheel and the surface, which dissipates energy. Note that only the last of these effects involves friction, therefore the name "rolling friction" is to an extent a misnomer.

The rolling resistance can be expressed as

F_r = c W (1)

where

F_r = rolling resistance or rolling friction (N, lb_f)

c = rolling resistance coefficient - dimensionless (coefficient of rolling friction - CRF)

W = m a_g

= normal force - or weight - of the body (N, lb_f)

m = mass of body (kg, lb)

a_g = acceleration of gravity (9.81 m/s², 32.174 ft/s²)

Rolling Resistance Coefficient
c	cl (mm)
0.001 - 0.002	0. 5	railroad steel wheels on steel rails
0.001		bicycle tire on wooden track
0.002 - 0.005		low resistance tubeless tires
0.002		bicycle tire on concrete
0.004		bicycle tire on asphalt road
0.005		dirty tram rails
0.006 - 0.01		truck tire on asphalt
0.008		bicycle tire on rough paved road
0.01 - 0.015		ordinary car tires on concrete, new asphalt, cobbles small new
0.02		car tires on tar or asphalt
0.02		car tires on gravel - rolled new
0.03		car tires on cobbles - large worn
0.04 - 0.08		car tire on solid sand, gravel loose worn, soil medium hard
0.2 - 0.4		car tire on loose sand

d. Tyre Pressure :

Car Tyres aren’t just unsafe when they’re old and worn out – you need to ensure you know what Tyre pressure you have in your Tyres when you drive it because there are critical safety and economic implications.

Car Tyre pressure is a measurement of how much air is in your pneumatic Tyre, and ensures the Tyres wear evenly and maintain the correct level of grip on the road surface. This is commonly expressed as PSI, or pounds-per-square-inch.

5.Force and Power required to push / pull an aircraft by a towing vehicle.

STUDY 5:

The force to move an air plane on an absolute flat runway with no wind at constant low speed is equal to the rolling resistance between the plane and the tarmac.

The rolling resistance for the air plane can be calculated as :

F_r = c m_r a_g (1)

where

F_r = rolling resistance (N, lb_f)

c = rolling resistance coefficient

m_r = rolling mass (kg, lb_m)

a_g = acceleration of gravity (9.81 m/s²)

The friction force for the puller can be calculated to

F_f = μ W

= μ m_f a_g (2)

where

F_f = frictional force (N, lb)

μ = friction coefficient

W = weight (N, lb_f)

m_f = friction mass (kg)

The drag force acting on the tow will be :

The drag force D exerted on a body traveling though a fluid is given by C is the drag coefficient, which can vary along with the speed of the body. But typical values range from 0.4 to 1.0 for different fluids (such as air and water).

ρ is the density of the fluid through which the body is moving.

v is the speed of the body relative to the fluid.

Now the tractive force or the pulling force required by the tow will be;

Pulling force = Drag force + friction force + Rolling resistance force

Now let us consider aircrafts with the following specifications :

Now as we have seen that various kinds of planes have different weights ,the amount of pulling force also will be different.

Therefore we will consider a range of weight :

Range of weight = 200 kgs - 250000 kgs '

The towing speed considered is 5 m/s

Area range : 50 - 100 m^2

Coefficient of rolling resistance : 0.02

Coefficient of friction : 0.01

Now we use a script from Matlab which will help us calculate the pulling force required :

clc
clear all

%Inputs
c=0.002%Rolling resistance coefficient
m=linspace(200,25000,2000) % Weight
g=9.81 %acceleration of gravity
u=0.6%friction coefficient
A=linspace(50,100,2000)%area of planes
v=2 % velocity
Cd=0.8 %Drag Coefficient

%Calculations

F1=c*m*g %Rolling resistance force
F2=u*g*m%Friction force
F3=0.5*A*1.2*Cd*(v)^2

Ft=F1+F2+F3

plot(m,Ft)
title('Tractive Force vs Weight of planes')
xlabel('Weight of planes(kg)')
ylabel('Tractive Force')
axis([0 2000 0 20000])

Results:

Part B:

6. (A). With necessary assumptions, calculate the force and power required to push / pull an aircraft by a towing vehicle.

STUDY 6(A):

In this study, we want to calculate the force and power required to push and pull an aircraft by towing vehicle so we take one of the towing vehicle model and airbus model on the website and consider the data for our calculation.

DOUGLAS TOWBARLESS AIRCRAFT TRACTOR: Model: TBL 280Mk4

The Douglas Tugmaster type TBL- 280 Mk4 towbar less aircraft handling tractor has been designed primarily for pushback, inter-gate towing, and longer distance maintenance towing operations at higher speeds with the following aircraft: -

• Embraer: ERJ 190/195
• McDonnell Douglas: DC9/MD80/MD90
• Boeing: B717, B737, B727, B757, B767, B787 and B777.
• Airbus: A318/A319/A320/A321, A310/A300, A330 and A340-200/300
• Boeing: DC10/MD11
• Lockheed: L 1011

• Maximum cradle lifting capacity = 35,000 kgs(Aircraft nose wheel weight).
• Length (Excluding Coupler) = 333” (8,470 mm) = 8.47m
• Width = 134” (3,400 mm) = 3.4m
• Wheel Base = 173” (4,400 mm) = 4.4m
• Height = 79" (2,000 mm) = 2m
• Tyre Size = R 22.5 = 571.5mm = 0.5715m
• Maximum Governed Speed = 20 mph (32 kph)

The coefficient of friction depends on the objects that are causing friction. The value is usually between 0 and 1 but can be greater than 1. A value of 0 means there is no friction at all between the objects. A value of 1 means the frictional force is equal to the normal force. It is a misconception that the coefficient of friction is limited to values between 0 and 1. A coefficient of friction that is more than 1 just means that the frictional force is stronger than the normal force.

Coefficient of rolling resistance([Math Processing Error]μrr) = 0.02 (Truck Tyre in asphalt concrete road)

Aircraft Model:

We are taking an aircraft model as Airbus A310 as considered as pushback operation. The advanced technologies of A310 and some specifications are given below,

The A310 helped pioneer the use of composites in commercial jetliners, with its vertical stabilizer built with carbonified materials that offer significant weight savings over conventional metallic structures. Other major applications of composites on the A310 include floor struts and panels, spoilers and main landing gear doors.

• Standard or Higher Gross Weight = 164000 kg
• Height = 15.80 m
• Width = 43.90 m
• Drag Coefficient ([Math Processing Error]Cd) = 0.02685

To Find:

The total force and power required to push/pull an aircraft by the towing vehicle.

Formula used:

Total Force (F) = [Math Processing Error]Frr + Fad

Rolling resistance Force ([Math Processing Error]Frr) = [Math Processing Error]μrr.m.g

Drag Force ([Math Processing Error]Fad) = [Math Processing Error]12.ρ.A.Cd.v2

Solution:

In the first step, we have to find out the rolling resistance force and air drag force for both towing vehicle and airbus to obtain the force and power value during the towing process,

To find rolling resistance force:

For Aircraft :

Rolling resistance force ([Math Processing Error]Frr1) = [Math Processing Error]μrr.m1.g

Where,

[Math Processing Error]μrr = Coefficient of rolling resistance of aircraft = 0.02

[Math Processing Error]m1 = mass of the aircraft = 164000 kg

g = gravitational force = 9.8 m/[Math Processing Error]s2

[Math Processing Error]∴([Math Processing Error]Frr1) = 0.02 x 164000 x 9.81

= 32176.80 N

For Towing Vehicle:

Rolling resistance force ([Math Processing Error]Frr2) = [Math Processing Error]μrr.m2.g

Where,

[Math Processing Error]μrr = Coefficient of rolling resistance of towing vehicle = 0.02

[Math Processing Error]m2 = mass of the towing vehicle = 35000 kg

g = gravitational force = 9.8 m/[Math Processing Error]s2

[Math Processing Error]∴(Frr2) = 0.02 x 35000 x 9.81

= 6909 N

So, the Rolling resistance force ([Math Processing Error]Frr) = [Math Processing Error]Frr1+Frr2

= 32176.80 + 6909

= 39085.80 N

To find Air drag force:

The Air Drag Force ([Math Processing Error]Fad) = [Math Processing Error]12.ρ.A.Cd.v2

Where,

[Math Processing Error]ρ = Density of air

A = frontal area of the vehicle on which the air strikes

v = velocity of the vehicle

[Math Processing Error]Cd = Drag Coefficient

For Aircraft :

Air Drag Force ([Math Processing Error]Fad1) = [Math Processing Error]12⋅ρ⋅A1⋅Cd1⋅v2

Where,

[Math Processing Error]ρ = 1.25 kg/[Math Processing Error]m3

[Math Processing Error]A1 = Height of the airbus x Width of the airbus = 15.80 x 43.90 = 693.62 [Math Processing Error]m2

Assume that vehicle running at the speed of 20 kmph.

[Math Processing Error]∴ v = (20 x [Math Processing Error]518) = 5.56 m/s

[Math Processing Error]Cd1 = Drag Coefficient of aircraft = 0.02685

[Math Processing Error]∴ ([Math Processing Error]Fad1) = [Math Processing Error]12 x 1.25 x 693.62 x 0.0265 x [Math Processing Error](5.56)2

= 355.137 N

For Towing Vehicle:

Air Drag Force ([Math Processing Error]Fad2) = [Math Processing Error]12.ρ.A2.Cd2.v2

Where,

[Math Processing Error]ρ = 1.25 kg/[Math Processing Error]m3

[Math Processing Error]A2 = Height of the towing vehicle x Width of the towing vehicle = 2 x 3.4 = 6.8 [Math Processing Error]m2

Assume that vehicle running at the speed of 20 kmph.

[Math Processing Error]∴ v = (20 x [Math Processing Error]518) = 5.56 m/s

[Math Processing Error]Cd2 = Drag Coefficient of the towing vehicle = 0.6

[Math Processing Error]∴ ([Math Processing Error]Fad2) = [Math Processing Error]12 x 1.25 x 6.8 x 0.6 x [Math Processing Error](5.56)2

= 78.82 N

So, the Air Drag Force ([Math Processing Error]Fad) = ([Math Processing Error]Fad1) + ([Math Processing Error]Fad2)

= 355.137 + 78.82

= 437.13 N

Now, the total force (F) = the Rolling resistance force ([Math Processing Error]Frr) + the Air Drag Force ([Math Processing Error]Fad)

= 39085.80 + 437.13

= 39522.93 N

Power required to push/pull the aircraft:

Power = Total Force x velocity

= 39522.93 x 5.56

= 219747.49 W

Therefore, Power = 219.74 kW

6. B. Develop the model for the calculated force and power using Simulink.

STUDY 6(B):

Force Calculation for Aircraft:

Force Calculation for Towing Vehicle:

Power requirement of Towing Vehice to push/pull the aircraft:

Model Explanation:

• Constant and gain blocks are used to feed the parameters such as mass, coefficient, and the other parameters.
• By using product block the resistive forces are calculated.
• By using the sum block the total forces are calculated.
• Lastly, the outputs are visualized by using display blocks.

7.A. Design an electric powertrain with type of motor, it’s power rating, and energy requirement to fulfill aircraft towing application in Simulink. Estimate the duty cycle range to control the aircraft speed from zero to highest. Make all required assumptions. Prepare a table of assumed parameters. Draw a block diagram of powertrain.

STUDY 7(A):

From the above Q.6, we have obtained the value of the power of towing vehicle to push/pull an aircraft with respect to our given velocity and now we have to find out the energy required for the vehicle.

Energy required for the vehicle:

Energy = Power x t

Where,

t = time taken for towing vehicle

Here, we consider the time taken for towing vehicle as about 20 minutes.

[Math Processing Error]∴ E = 219.74 x [Math Processing Error](12003600)

E = 73.24 kWh

The above data shows how much power is taken at the speed of 20 kmph and how much energy is consumed in 20 minutes of time.

In this case, we have to find out the input power to drive the duty cycle of the towing vehicle. The output power is considered from the study-6 that values are based upon certain assumptions and calculations from the towing vehicle model as Douglas Tugmaster type TBL-280 Mk4 from the website.

The formula for duty cycle is given below,

Duty cycle = Power input/Power output

We know,

Power = Voltage x Current

Here we consider,

Input Voltage supply (Motor Specification) = 400 V

Input Current Value = 620 A

Now substitute the voltage and current value in the power formula to get the input power data,

Power input = 400 x 620 = 248000 W

By converting the unit of power from W to kW we get,

Power input = 248 kW

Therefore we have obtained power input and power output now substitute these values in the duty cycle formula we get,

Duty cycle = Power output/Power input

= 219.74/248

= 0.886

So, The duty cycle for the towing vehicle Douglas Tugmaster type TBL-280 Mk4 is 88.6%. This duty is obtained for our system based upon several assumptions.

Block Diagram of Electric Powertrain:

7. (B). Also, Design the parameters in an excel sheet.

STUDY 7(B):

Assumed Parameter for an aircraft model as Airbus A310
Gross Weight [mass] (kg)				164000
Coefficient of Roling Resistance [Urr]				0.02
Air Density [rho] (kg/m^3)				1.25
Drag Coefficient [Cd]				0.02685
Frontal Area [A] (m^2)				693.62
Velocity (m/s)				5.56
Gravitational Force (m/s^2)				9.81
Assumed Parameter for Towing vehicle TBL-280 Mk4
Gross Weight [mass] (kg)				35000
Coefficient of Roling Resistance [Urr]				0.02
Air Density [rho] (kg/m^3)				1.25
Drag Coefficient [Cd]				0.6
Frontal Area [A] (m^2)				6.8
Velocity (m/s)				5.56
Run Time for Towing Vehicle (mins)				20
Gravitational Force (m/s^2)				9.81
Motor Parameters
Motor Type				REB 90
Motor Voltage (V)				400
Motor Rating (kW)				60
Working Rotation (rpm)				1500
Max. Torque (N-m)				300
Weight (g)				22000
Cooling				Air
Battery Parameters
Battery Input Voltage (V)				620
Force Calculation for Aircraft
Rolling Resistance Force [Frr1] (N)				32176.80
Aerodynamic Drag Force [Fad1] (N)				359.83
Force Calculation for Towing Vehicle
Rolling Resistance Force [Frr2] (N)				6867
Aerodynamic Drag Force [Fad2] (N)				78.83
The Total Force [F] (N)				39482.46
Power required to push/pull the Aircraft [P] (kW)				219.52
Energy Calculation for Towing Vehicle
Energy [E] (kWh)				73.17415573
Power Input (kW)				248
Duty Cycle				88.52%

Conclusion:

Therefore, all the various studies about the aircraft are analyzed, and calculations to find the force and power required to push/pull an aircraft by a towing vehicle and energy requirement to fulfill aircraft towing application are also determined. The values of the mathematical expression from Q.6 and Q.7 are given below,

Power = 219.74 kW

Energy = 73.24 kWh

Duty Cycle = 88.6%