Powertrain for aircraft in runways
PROJECT : POWERTRAIN FOR AIRCRAFT IN RUNWAYS
AIM OF THE PROJECT:
- Detailed overview of air-craft and its parts.
- Modelling and estimation of necessary parameters required to control the motion of aircraft in runways.
- Observing the behaviour of aircrafts motion in grounf and during take-off.
Objective:
- 1. Search and list out the total weight of various types of aircrafts.
- 2. Is there any difference between ground speed and air speed?
- 3. Why is it not recommended to use aircraft engine power to move it on the ground at Airport?
- 4. How an aircraft is pushed to runway when its ready to take off?
- 5. Learn about take off power, tyre design, rolling resistance, tyre pressure, brake forces when landing.
- 6. A. With necessary assumptions, calculate the force and power required to push / pull an aircraft by a towing vehicle.
- B. Develop the model for the calculated force and power using Simulink.
- 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.
- (Hint :DC7 Block)
- B. Also, Design the parameters in excel sheet.
Solution:
STUDY 1: As we know that ,weight is the force generated by the gravitional attraction of the earth which we can estimate by the given formula w=m*g, where w=is the weight, m is the mass, g is the gravitational constants g=9.8m/sec^2 or 32.2ft/sec^2 . In case of a whole aircraft there are different parts and each part of the aircraft bears a unique weight and mass example : the wings, the engines, the payload, and the fuel.The mass of the individual components can be calculated if we know the size of the components and its chemical composition example: iron, plastic, aluminium, gasoline etc. Therefore, the total weight of the aircraft is the sum of the individual components given as: W=w(Fuselage)+w(Payload)+w(Engines)+w(Wings)+....
It can be pictured as :-

Center of gravity (CG) of an aircraft is calculated as follows:
- Determine the weights and arms of all mass within the aircraft.
- Multiply weights by arms for all mass to calculate moments.
- Add the moments of all mass together.
- Divide the total moment by the total mass of the aircraft to give an overall arm.
The arm that results from this calculation must be within the center of gravity limits dictated by the aircraft manufacturer. If it is not, weight in the aircraft must be removed, added (rarely), or redistributed until the center of gravity falls within the prescribed limits.
Aircraft center of gravity calculations are only performed along a single axis from the zero point of the reference datum that represents the longitudinal axis of the aircraft (to calculate fore-to-aft balance). Some helicopter types utilize lateral CG limits as well as longitudinal limits. Operation of such helicopters requires calculating CG along two axes: one calculation for longitudinal CG (fore-to-aft balance) and another calculation for lateral CG (left-to-right balance).
The weight, moment and arm values of fixed items on the aircraft (i.e. engines, wings, electronic components) do not change and are provided by the manufacturer on the Aircraft Equipment List. The manufacturer also provides information facilitating the calculation of moments for fuel loads. Removable weight items (i.e. crew members, passengers, baggage) must be properly accounted for in the weight and CG calculation by the aircraft operator.
| Mass (lb) | Arm (in) | Moment (lb-in) | |
|---|---|---|---|
| Empty aircraft | 1,495.0 | 101.4 | 151,593.0 |
| Pilot and passengers | 380.0 | 64.0 | 24,320.0 |
| Fuel (30 gallons @ 6 lb/gal) | 180.0 | 96.0 | 17,280.0 |
| Totals | 2,055.0 | 94.0 | 193,193.0 |
To find the center of gravity, we divide the total moment by the total mass: 193,193 / 2,055 = 94.01 inches behind the datum plane.
Aircraft authorised gross weight is defined as the total aircraft weight at any moment during the flight or ground operation. The authorised weight limits that can be legally be used by any operator or airline are listed in the AFM and the weight and balance manual. They are also referred as purchased weights.
The classification of different types of weight under gross weight can be made in the following categories:
- Maximum ramp weight(MRW):- It is defined as the maximum weight authorised for taxiing or towing on the ground as limited by aircraft strength or airworthiness requirements. The difference between the maximum ramp weight and the maximum take-off weight depends on the size of the air-craft, the number of engines , APU operation and engine fuel consumption. Which is typically assumed for 10-15 minuts of taxiing, towing of run-up operations.
- Maximum take-off weight(MTOW):- It is defined as the maximum certified design weight for take-off run as limited by air-craft strength and aieworthiness requirement. the maximum take-off weight is always less than the maximum ramp weight to allow fuel burned during taxi by the engines and the APU.
- Maximum landing weight(MLW):- It is defined as the maximum design certified weight for normal landing of the aircraft. It mainly depends on the landing gear strength or the landing impact loads on certain parts of the wing and chassis structure.
- MDLW<MDTOW<MRW
- Maximum zero fuel weight(MZFW):- The maximum zero fuel weight is the maximum certified of the aircraft without the usable fuel and others limited by aircraft strength and airworthiness requirements. In other word it is the maximum weight permitted before the usable fluid and other usable items are loaded in the aircraft.
- Operational empth weight(OEW):- The OEW is fixed for a specific aircraft and only gets changed during operational changes and maintenance. OEW is the empty weight that is used in flight simulator or usuall planning software.
- Actual zero fuel weight(AZFW):- If we add the payload to the Empty plane weight then we get the actuall zero fuel weight. Basically the payload includes the passenger luggage weight and cargo weight given by the following relationship.
- Minimum Flight weight(MFW):- Minimum certified weight for flight as limited by aircraft strength and airworthiness requirements. The total weight of an aircraft includes aircrafts's empth weight +payload.
- Aircrafts's empty weight:- The aircraft weight with fuel left in tank +engine oil +other operating fluids
- Payload:- The fuel weight+ passengers weight +other operating fluids.
| Operational empty weight(OEW) |
+
| Payload |
=
| Actuall zero fuel weight(AFZW) |
| Aircraft type | Maximum take-off weight(kg) | Maximum fuel(kg) |
| Boeing707-320 | 151500 | 72503 |
| Boeing747-200 | 52610 |
14520 |
| AirbusA300-B4 | 165000 |
46654 |
| Boeing757-200 | 115650 | 36260 |
| DouglasDC-8-32 | 140000 | 31020 |
| Boeing767-400 | 209111 | 73363 |
| Boing737-900 | 79016 |
20894 |
| AirbusA340-600 | 368000 | 156487 |
| The embraer phenom 300 | 8000 | 1545 |
Part A:
- Search and list out the total weight of various types of aircrafts.
Ans.
Classification of aircrafts are as below:




According to the purpose, principle, types of wings, material and components used, the size and weight of the aircraft varies as mentioned in above flowcharts.
2. Is there any difference between ground speed and air speed?
Ans. True airspeed is simply the speed at which an aircraft is moving relative to the air it is flying in. As such, it’s also the speed at which the air is flowing around the aircraft’s wings.
Ground speed, on the other hand, is the aircraft’s speed relative to the ground. One thing that should be noted here is that it’s its horizontal rather than vertical speed – an aircraft climbing completely vertically would have a ground speed of zero.
In other words, while airspeed is what determines whether there is enough airflow around an aircraft to make it fly, ground speed is what determines how fast an aircraft will get to its destination.

Airspeed = Ground Speed - Wind Speed

On a perfectly still day, the airspeed is equal to the ground speed. But if the wind is blowing in the same direction that the aircraft is moving, the airspeed will be less than the ground speed.
3.Why is it not recommended to use aircraft engine power to move it on the ground at Airport?
Ans. Although many aircraft are capable of moving themselves backward on the ground using reverse thrust (a procedure referred to as a power back), the resulting jet blast or prop wash 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 towing is therefore the preferred method to move the aircraft away from the gate. Unless the aircraft is in a location where it is unwise to taxi under aircraft power and necessitating a tow by a large tractor, the aircraft’s engine(s) is how the craft moves. Obviously, it is prudent to use only the amount of power to get the airplane moving and then reduce the power for taxiing to avoid high volumes of air spreading debris or damaging other aircraft or ground vehicles.
Whether jets or prop airplanes, we use the aircraft’s (engine) power to move on the airfield.

fig - Aircraft towing by a truck
Jet blast is the phenomenon of rapid air movement produced by the jet engines of aircraft, particularly on or before take-off. Jet blast can be a hazard to people or other unsecured objects behind the aircraft and is capable of flattening buildings and destroying vehicles.
Despite the power and potentially destructive nature of the jet blast, there are relatively few jet blast incidents. Due to the invisible nature of the jet blast and the aerodynamic properties of light aircraft, light aircraft moving about airports are particularly unsafe. Pilots of light aircraft frequently stay off to the side of the runway, rather than follow in the center, to negate the effect of the blast.
Towing with Taxibot saves precious fuel and reduces engine wear and tear. The ignition will be turned only when the aircraft reaches the runway. The usage of Taxibots will significantly bring down the consumption of fuel by as much as 85 percent used during taxiing of an aircraft. Taxi boats will also help in decongesting boarding gates and the apron area by providing efficient pushbacks.
So, due to the noise and fumes plus they burn a lot of fuel aircrafts are towed into a spot due to it being a small parking space for safety.
4. How an aircraft is pushed to runway when its ready to take off?
Ans.
Pushback is when an aircraft is pushed backwards away from the airport gate by vehicles called tugs or tractors.
Closer to departure, an aircraft tug will park right in front of the nose wheel.
The tug might be directly attached to the plane's nose gear with a tow bar, or could be a "wheel-lift" tug. These tugs cradle the nose gear, then lift it up before moving the plane. That gives the tug driver control over the plane's direction during pushback.
New taxi technologies are appearing, like pilot-controlled tugs, and electric motors mounted to the plane's landing gear. Both promise to save fuel, and reduce airport noise.
Takeoff is the phase of flight in which an aircraft goes through a transition from moving along the ground (taxiing) to flying in the air, usually starting on a runway. Usually the engines are run at full power during takeoff. Following the taxi motion, the aircraft stops at the starting line of the runway. Before takeoff, the engines, particularly piston engines, are routinely run up at high power to check for engine-related problems. This makes a considerable noise. When the pilot releases the brakes, the aircraft starts accelerating rapidly until the necessary speed for take-off is achieved.
The takeoff speed required varies with air density, aircraft weight, and aircraft configuration (flap and/or slat position, as applicable). Air density is affected by factors such as field elevation and air temperature.
Operations with transport category aircraft employ the concept of the takeoff V-Speeds, V1 and V2. These speeds are determined not only by the above factors affecting takeoff performance, but also by the length and slope of the runway. Below V1, in case of critical failures, the takeoff should be aborted; above V1 the pilot continues the takeoff and returns for landing. After the co-pilot calls V1, Then, V2 (the safe takeoff speed) is called. This speed must be maintained after an engine failure to meet performance targets for rate of climb and angle of climb.
The speeds needed for takeoff are relative to the motion of the air (indicated airspeed). A head wind will reduce the ground speed needed for takeoff, as there is a greater flow of air over the wings. This is why the aircrafts always take off against the wind. Side wind is not preferred as it would disturb the stability of the aircraft. Typical takeoff air speeds for jetliners are in the 130–155 knot range (150–180 mph, 240–285 km/h). For a given aircraft, the takeoff speed is usually directly proportional to the aircraft weight; the heavier the weight, the greater the speed needed. Some aircraft have difficulty generating enough lift at the low speeds encountered during takeoff. These are therefore fitted with high-lift devices, often including slats and usually flaps, which increase the camber of the wing, making it more effective at low speed, thus creating more lift. These have to be deployed from the wing before performing any maneuver.
At the beginning of the climb phase, the wheels are retracted into the aircraft and the undercarriage doors are closed. This operation is audible by the passengers as a noise coming from below the floor.
5. Learn about take off power, tyre design, rolling resistance, tyre pressure, brake forces when landing.
Ans.
TAKEOFF POWER:
An airplane is motionless at the end of a runway. This is denoted by location O. The pilot releases the brakes and pushes the throttle to maximum takeoff power, and the airplane accelerates down the runway. At some distance from its starting point, the airplane lifts into the air. The distance the airplane cover along the runway before it lifts into the air is called the ground roll (sg). The total takeoff distance also includes the extra distance covered over the ground after the airplane is airborne but before it clears an obstacle of 50 ft for military aircraft and 35 ft for commercial aircraft. This is denoted by sa. The sum of sg and sa is the total takeoff distance.

ROLLING RESISTANCE:
Rolling resistance R, caused by friction between the tires and the ground.

TYRE DESIGN:
The tire manufacturer with the size and weight requirements, the tire manufacturer begins the process of designing a tire that meets the needs of the aircraft manufacturer as well as all regulatory requirements — including foreign regulations in many cases.
Engineers are challenged with designing tires with cool running, heat-resistant materials while simultaneously exceeding tire service requirements. Tire prototypes are put through rigorous tests that simulate cycles of landings, take-offs, and taxi operations. It is only after the tires pass all mandatory tests and meet the requirements of the aircraft manufacturer and airworthiness authorities that the tires are put into production.
Two types of tires are used in aircraft applications — bias-ply tires and radial tires.

Bias-ply tire construction:
The tire construction consists of the following components:
Tread: The tread is made of rubber mixed with other additives to obtain the desired level of toughness, durability, and resistance to wear. The tread pattern is designed to aircraft operational requirements, with the ribbed tread design used widely due to its good traction under varying runway conditions.
Sidewall: The sidewall is a protective layer of rubber that covers the outer casing ply. It extends from the tread edge to the bead area.
Tread Reinforcing Ply: One or more layers of fabric that strengthens and stabilizes the tread area for high-speed operation.
Buff Line Cushion: The buff line cushion is made of rubber compound to enhance the adhesion between the tread reinforcing ply and the breakers or casing plies.
Breakers: Breakers are reinforcing plies of rubber-coated fabric placed under the buff line cushion to protect casing plies and strengthen and stabilize the tread area.
Casing Plies: Alternate layers of rubber-coated fabric (running at opposite angles to one another) provide the strength of the tire.
Wire Beads: Hoops of high tensile strength steel wire that anchor the casing plies and provide a firm mounting surface on the wheel. The outer edge of the bead that fits against the wheel flange is called the bead heel. The inner bead edge is called the bead toe.
Apex Strip: A wedge of rubber affixed to the top of the bead bundle.
Flippers: Layers of rubberized fabric that help anchor the bead wires to the casing and improve the durability of the tire.
Ply Turnups: The casing plies are anchored by wrapping them around the wire beads, thus forming the ply turnups.
Chafer: A protective layer of rubber and/or fabric located between the casing plies and wheel to minimize chafing.
Liner: In tubeless tires, the liner is a layer of low permeability rubber that acts as a built-in tube and restricts gas from diffusing into the casing plies. In tube-type tires, a thinner liner is used to prevent tube chafing against the inside ply.
Radial-ply tire construction
With their rigid belt, they provide increased landings and reduced rolling resistance. They have fewer components in their construction and are lighter than similarly sized bias ply tires. Components that differ from bias-ply construction as follows:
Overlay: A layer of reinforcing rubber coated fabric placed on top of the belts to aid in high speed operation.
Belt Plies: A composite structure that stiffens the tread area for increased landings. The belt plies increase the tire strength in the tread area.
Casing Plies: As in bias-ply tires, the casing plies are layers of rubber-coated fabric. However, unlike those in bias plies that run at opposite angles to one another, radial plies run radially from bead to bead.
Chippers: The chippers are layers of rubber-coated fabric applied at diagonal angles that improve the durability of the tire in the bead area.
TYRE PRESSURE:
Aircraft tires generally operate at high pressures, up to 200 psi (14 bar; 1,400 kPa) for airliners, and even higher for business jets. Each of the twelve Boeing main tires is inflated to 220 psi (15 bar; 1,500 kPa), weighs 120 kg (260 lb), has a diameter of 134 cm (53 in).

BRAKE FORCES WHILE LANDING:
aircraft are equipped with an autobrake system that controls the deceleration of the aircraft by automatically optimizing the application of brake force independent of pilot operation of the brake pedals to minimize stopping distance, reduce pilot workload and smooth braking action. Another common feature of aircraft brake systems is a skid control function. Similar to anti-lock brakes on an automobile, skid control systems prevent wheel lockup. They minimize stopping distance and prevent the negative effects of skidding on tires such as unnecessary tire wear and blowout. Skid control is accomplished by applying an optimal brake force that maximizes the coefficient of friction and remains just below the amount of force that would cause skidding. In one implementation, the proper force is arrived at by continuously sensing wheel speed and comparing it to a calculated aircraft velocity. The difference between the two values represents wheel slip and brake force is reduced if it rises above a specified value.
Part B:
- A. With necessary assumptions,calculate the force and power required to push/pull an aircraft by a towing vehicle. B.Develop the model for the calculated force and power using Simulink.
Ans.
A.
Assumptions:
- Kerb weight of aircraft=60000Kg
- Payload=10000 Kg
- Towing vehicle weight=8000Kg
- Rolling friction coefficient for dry concrete= 0.03
- Acceleration due to gravity=9.81m/s^2
- Frontal area of aircraft=20m^2
- Velocity of towing vehicle=20 km/h
- Coefficient of drag for aircraft=0.19
- Coefficient of drag for towing vehicle=0.6
- Density of air=1.225 kg/m^3
For above mentioned parameters, the force required is calculated as 23.254kN and power required is 129.189kW.

B. SIMULINK MODEL for force and power calculation is:

- Assumed parameters are given to the model using Constant blocks.
- Using add and multiply blocks, the formulae for rolling resistance force and Aerodynamic drag are calculated.
- Using Add block, the overall force is determined.
- By mulitplying force with velocity, power is calculated.
- The values of force and power are displayed using Display block.
- 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.
(Hint :DC7 Block)
B. Also, Design the parameters in excel sheet.
Ans.
BLOCK DIAGRAM FOR POWER TRAIN:

SIMULINK DIAGRAM FOR POWER TRAIN:

Input: Signal builder

The output waveforms are:

Assumed parameters:
|
Force required to push/pull |
23.254kN |
|
Power required |
129.189kW |
|
Radiurs of tyre |
25inch =0.635m |
|
Gear ratio |
8 |
|
Transmission efficiency |
87% |
|
Motor efficiency |
95% |
|
Time taken by towing operation |
10 min |
Torque required for wheels= Total force*radius = 23254*0.635Nm = 14766Nm
Motor torque= Wheel torque/(gear ratio *transmission efficiency)
=14766/(8*0.87)
=2121.55Nm
Required motor torque= 2121.55/0.95
=2198.09Nm
Total power required =129.189/(0.87*0.95)
=156.31kW
Energy required= Total power *time =156.31*10/60 =26.05kWh
Let us consider rated power is 220kW
Then, duty cycle= Power required/ Rated power
= 156.31/220
=0.71
Therefore, duty cycle range is from 0% to 71%
B.
IMPLEMENTATION IN EXCEL
STUDY 2:> AIR-SPEED Vs GROUND- SPEED
Ground speed: It is the horizontal speed of an aircraft relative to the ground. An aircraft heading vertically would have a ground speed of zero. Ground speed can be determined by the vector sum of the aircraft's true airspeed and the wind speed and the direction of motion.
Wind speed: If we pick a reference point on the ground, the air moves relative to the reference point at the wind speed. A positive velocity is defined in the direction od the aircraft's motion.
Airspeed: The important part in the generation of lift of aircraft is the relative velocity between the object and the air, which is called air-speed. It cannot be directly measured from the ground position , it is computed from the ground speed and wind speed. it is the vector difference betwen the ground speed and the wind-speed.
As we know, that the air craft usually operates in ground as well as in air. so, the ground speed and air-speed usually change based on the wind component. If we consider that there is no wind component then, ground speed= air-speed. If the wind is blowing in the tail-directionof the aircraft then airspeed is greater than wind speed(air-speed=ground-speed+wind speed). If the wind is blowing in the Head direction of the air-craft then airspeed is less than ground speed. So, airspeed= groundspeed-wind speed. gravity also plays a major role in increasing the aircrafts's speed while its desending. If the measured Airspeed is greater than observed ground speed then the wind speed becomes positive. here wind speed is the vector difference between ground and Air-speed. If in case the wind is zero it is equall to ground-speed.
STUDY 3:> Why is it not recommended to use aircraft engine power to move it on the ground at Airport?
The Engine of the aircraft can easily do the work under its ow power to go towards runaways and after landing taxi to their assigned gate. But, as we know that the engine is so powerfull that the thrust developed produces jet blast which might cause damage to the terminal building or various people and equipment. Engines which are close to the ground may also blow sand and debris back and forth which may get sucked to the engine. A pushback is therefore the preferred method to move the air-craft away from the gate and most importantly it reduces the cost of aviation fuel. Taxing can save a lot of money.
- There is a risk of injury to ground support personnel who may be in relatively close to the air-craft.
- It is easier for the truck driver to see the surroundings better than the pilot who is sitting in the cock-pit wit limiting window. the pushback driver knows the airport better than the pilot.
- Effectively a loss of control can happen, especially during high power engine running. Damage can occur to the air-craft itself,other aircraft nearby and other buildings.
- A new system was proposed where a new system in which a push-back truck will move the air-craft all the way to run-way to save fuel and reduce impact of environment.
- The plane engines are very loud, when more than one plane will addup their sound, then it will be unbearable for passengers and other parts near airport.
STUDY 4:> HOW AN AIRCRAFT IS PUSHED TO RUNWAY WHEN ITS READY TO TAKE-OFF ?

TAXIING :
It is defined as the movement of the air-craft on the ground, under its own power where as towing or pushback is where the air-craft is moved by the tug. The air-craft usually moves on wheels but the term also used for the air-craft that has skies or floating equipments. An airplane uses taxiways to taxi from one-place on the air-port to another, example when the air-craft moves from hanger to the runaway.
TOWING :
STUDY 5:>
TAKE-OFF POWER:
In the case of light aircraft full power is used during take-off and in large aircrafts like airliner use a reduced level power to take-off,where less than full power is used to prolong the engine durability. before take-off the piston engines are run routinely at high power to check engine related problems.The nose is raised to a nominal 5-15 degree nose up pitch alltitude toincrease lift from the wings and effect lift off. The takeoff power is controlled in such a way that it can cover 35 feet screen height plays in the take-off. The pilot needs to look around different distances that affect the take-off performance which are:
- TAKE-OFF RUN AVAILABLE(TORA): The distance from which the air-craft can start its take-off run to the point till the end marking for surface change.
- THE CLEARWAY: This is the area st the end of TORA that is free from buildings trees or any other obstructions .The aircraft can use this area to acheive 35 feet sceen height.
- ACCELERATE-STOP DISTANCE AVAILABLE(ASDA): The final distance that must be considered for take-off performance is the ASDA, This distance of weight bearing surface is available to the air-craft to accelerate and then come to stop in case of emergency.
- Take-off power= Force*Displacement i.e (m*dv/dt)*2*S1=> (T-D-F)*S1, where S is the runway length. The forces involved are T= thrust of propulsion system, D= Aerodynamic drag which the vehicle resists, F= rolling resistance due to the contavt on wheels on the ground
TIRE DESIGN:
The tire design of an aircraft may seem a challenging job, because the tyre has to withstand heavy loads while landing, take-off, taxiing and parking. The number of wheels required for an aircraft increases as the weight of the aircraft increases cause it should be distributed evenly. The tyre generates a lot of heat during landing because it drags the wheel to match its momentum. The tyre is designed in such away that it withstands hugh crosswind conditions, extreme pressure and to prevent hydroplanning and for increased braking effect.
There are two types of construction of tyres which are :
Radial tyre: It has fiber strands of the poly fabric at 90degree to the direction of rotation and the tyre side-wall. This restricts flexibility of the bi-deirectional sidewall while it strengthnes the tyre to carry heavy loads . Due to their unique construction radial tyres are resistant to penetration and cuts. Due to stiffer threads they distribute weight evenly. Thus provide greater traction and helps in preventing heat.
Bias tyre: It has the fabric bias oriented with and cross the direction of rotation and the side-wall. Since the fabric stretches, the tire is flexible and can absorb loads, the cut resistnt area is the sidewalls, strength is obtained by adding piles, these tyres doesn't absorb heat well.

Rolling resistance:
It is defined as the force resisting the motion when a body rolls on a surface (ex- ball, tyre) .Rolling resistance can be seen in an aircraft when the air-craft takes off from the runway and while landing on the runway.
rolling resistance force can be written as: Frr=Urr*m*g(N)
Where Urr= coefficient of rolling resistant
m= Mass(kg)
Frr= rolling resistance (N)
g= acceleration due to gravity(9.81m/s^2)
Tyre pressure:
The tyres of an air-craft have to withstand very high amounts of pressure, while take-off, landing, towing, taxing. as the weight of the aircraft increases the no. of wheels are also increased.as we know that while landing the aircraft drags the wheel till it matches with its rotational velocity, due to this a lot of heat is generated due to friction. aircraft tires are usually filled with nitrogen to minimize expansion and contraction from changes in tempretures and pressure during flight , Also the use of inert gasses for tire inflation reduces the possibility of tire explosion. services should be done regularly by checking tyre pressures and maintaining proper tire inflation pressure.
Rolling resistance and tire pressure are inversely proportional to each other.
Brake devices used during landing:
- Wheel brakes(Anti-skid and Auto-brakes): Aircraft have highly-engineered, multi-disc brakes made of a carbon-steel material. Manufacturers include Honeywell and Goodrich, part of Collins Aerospace. In general, the brakes are composed of discs that rotate with the wheel and separate discs that are fixed. When pressure is applied from the right fixed disc on all of the discsthe entire assembly compresses to create the braking action. Carbon brakes are standard today; they cool faster than steel brakes (their predecessor) and can weigh up to 700 pounds less. For the initial part of the braking, say down to around 70 knots, we let the autobrakes do the job, but after that we have to come onto the toe brakes to disengage the autobrake The transition from autobrake to manual brakes can be quite difficult to do smoothly especially in a crosswind, as you will be steering the aircraft with the rudder pedals and then have to press down on the tops of the rudder pedals evenly to deactivate the autobrakes and start manual braking.

- Spoilers: when the wheels touch the ground, a set of spoilers raise up quickly, which kills the lift provided by the wings. (There are two sets seen in the image below: ground spoilers that only deploy on landing, and spoilers that are used in flight as speed brakes as well as on landing.) While the spoilers provide some drag, their primary purpose is to stop the plane from actually flying, putting all of the weight on the landing gear and in turn making the brakes that much more effective.

- Reverse thrust: he final element of braking action is the thrust reversers. In a modern high-bypass turbofan engine, a full 90 percent of the air passing through the engine is simply sucked in, sped up and pushed out of the engine without mixing the fuel. In these engines, ducts on the side of the engine open up and direct that air out and nearly forward, opposite the direction of travel. This is called a cold-stream reverse thrust, and is part of the engine design of most modern engines. (You may have also seen clam-shell style reverse thrusters on older aircraft, which cup the back of the engine.)

STUDY 6:> A. With necessary assumptions, calculate the force and power required to push / pull an aircraft by a towing vehicle
B. Develop the model for the calculated force and power using Simulink.
Solution: Considering the parameters for airbus a380, assumed towing vehicle weight 1000kg


Here, the minimum power required for the towing vehicle to push/pull an aircraft of the given specifications is 45.60kw .So we took the above assumed parameters and developed a simulink model.

- Here we see that the output in the display is 45.653kw.
- Constant blocks are used to feed the parameters such as mass, coefficients and others
- Using sum block total resistant forces are calculated
- Display is used for visuals
STUDY 7:>
- 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.
- Design the parameters in excel sheet.
Solution:
SIMULINK MODEL OF POWERTRAIN OF AN AIR-CRAFT TOWING VEHICLE:

Estimation of Duty cycle: As we know that the power required for towing vehicle to push/pull is equall to 45.60kW. For this model we have considered the motor REB 90 for drive train.

Considering 60kW as continous power, so the voltage will be 400V. Battery power is considered to be 550V. we know that duty cycle is given by d=Vo/Vb. d=400/550, => 0.7272. There will also be losses due to the resistance of FET and inductance. Correction factor is considered to be 90% ,that makes us consider that there is 10% loss, So the voltage which is demanded by the motor should be 10% more than the required voltage.[d =0.7272*(1+0.1)= 0.799~0.8. so here the voltage demand is 440V from the battery.
| Mass of the aircraft | 5,80,000kg |
| Mass of towing vehicle | 1000kg |
| Coefficient of rolling resistance | 0.002 |
| Drag coefficient | 0.025 |
| Air-density | 1.125kg/m^3 |
| Frontal area | 150m^2 |
| Velocity | 4m/s |
| Uphill gradient | 0 deg |
| Battery voltage | 550V |
| Correction factor | 0.8 |
INPUT:

OUTPUT FROM THE BATTERY :

Output from the motor:

After simulating the model the parameters are stated in excel sheet:
