Project-1: Powertrain for aircraft in runways

1.

MTOW = Maximum take-off weight, MLW = Maximum landing weight, TOR = Take-off run (SL, ISA+15°, MTOW), LR = Landing run (SL, ISA+15°, MLW)

​

Type	MTOW [kg]	MLW [tonnes]	TOR [m]	LR [m]	ICAO category	FAA category
Antonov An-225	640,000	591.7	3500		Heavy	Super
Scaled Composites Model 351 Stratolaunch	589,670		3660		Heavy	Super
Airbus A380-800[1][2][3]	575,000	394	3100	1930	Super	Super
Boeing 747-8F	447,700	346.091	3100	1800	Heavy	Heavy
Boeing 747-8	443,613	306.175	3100		Heavy	Heavy
Boeing 747-400ER	412,770	295.742	3090		Heavy	Heavy
Antonov An-124-100M	405,060	330	2520	900	Heavy	Heavy
Boeing 747-400	396,900	295.742	3018	2179	Heavy	Heavy
Lockheed C-5 Galaxy	381,000	288.417	2530	1494	Heavy	Heavy
Boeing 747-200	377,840	285.700	3338	2109	Heavy	Heavy
Boeing 747-300	377,840	260.320	3222	1905	Heavy	Heavy
Airbus A340-500	371,950	240	3050	2010	Heavy	Heavy
Airbus A340-600	367,400	256	3100	2100	Heavy	Heavy
Boeing 777F	347,800	260.816	2830		Heavy	Heavy
Airbus A330-900	352,000	251.5	3100		Heavy	Heavy
Boeing 777-300ER	351,800	251.29	3100		Heavy	Heavy
Boeing 777-200LR	347,450	223.168	3000		Heavy	Heavy
Boeing 747-100[7]	340,200	265.300			Heavy	Heavy
Airbus A350-1000	308,000	233.5			Heavy	Heavy
Boeing 777-300	299,370	237.683	3380		Heavy	Heavy
Boeing 777-200ER	297,550	213.00	3380	1550	Heavy	Heavy
Airbus A340-300	276,700	190	3000	1926	Heavy	Heavy
McDonnell Douglas MD-11	273,300	185	2990	1890	Heavy	Heavy
Airbus A350-900	270,000	175	2670	1860	Heavy	Heavy
Ilyushin Il-96M	270,000	195.04	3115	2118	Heavy	Heavy
McDonnell Douglas DC-10	256,280	183	2990	1890	Heavy	Heavy
Boeing 787-9	254,000	192.777	2900		Heavy	Heavy
Boeing 787-10	254,000	201.849			Heavy	Heavy
Airbus A340-200	253,500	181	2990		Heavy	Heavy
Ilyushin IL-96-300	250,000	175	2600	1980	Heavy	Heavy
Airbus A330-300	242,000	185	2500	1750	Heavy	Heavy
Airbus A330-200	242,000	180	2220	1750	Heavy	Heavy
Lockheed L-1011-500	231,300	166.92	2636		Heavy	Heavy
Boeing 787-8	228,000	172.365	3300	1695	Heavy	Heavy
Lockheed L-1011-200	211,400				Heavy	Heavy
Ilyushin IL-86	208,000	175			Heavy	Heavy
Boeing 767-400ER	204,000	158.758	3414		Heavy	Heavy
Airbus A300-600R	192,000	140	2385	1555	Heavy	Heavy
Boeing 767-300ER	187,000	136.08	2713	1676	Heavy	Heavy
Concorde	185,000	111.1	3440	2220	Heavy	Heavy
Airbus A300-600	163,000	138	2324	1536	Heavy	Heavy
Boeing 767-300	159,000	136.078	2713	1676	Heavy	Heavy
Airbus A310-300	157,000	124	2290	1490	Heavy	Heavy
Vickers VC10	152,000	151.9			Heavy	Heavy
Boeing 707-320B	151,000	97.5			Heavy	Heavy
Boeing 707-320C	151,000	112.1			Heavy	Heavy
Douglas DC-8-61	147,000				Heavy	Heavy
Airbus A310-200	142,000	123	1860	1480	Heavy	Heavy
Airbus A400M	141,000	122	980	770	Heavy	Heavy
Douglas DC-8-32	140,000				Heavy	Heavy
Douglas DC-8-51	125,000				Medium	Large
Boeing 757-300	124,000	101.6	2550	1750	Medium	Large
Boeing 707-120B	117,000	86.3			Medium	Large
Boeing 757-200	116,000	89.9	2347	1555	Medium	Large
Boeing 720B	106,000	79.5			Medium	Large
Boeing 720	104,000	79.5			Medium	Large
Tupolev Tu-154M	104,000	80			Medium	Large
Tupolev Tu-204SM	104,000	87.5	2250		Medium	Large
Convair 880	87,500				Medium	Large
Boeing 737-900	85,000	66.36	2500	1704	Medium	Large
Boeing 737-900ER	85,000	71.35	2804	1829	Medium	Large
Boeing 727-200 Advanced	84,000	70.1			Medium	Large
Airbus A321-100	83,000	77.8	2200	1540	Medium	Large
Boeing 737-800	79,000	65.32	2308	1634	Medium	Large
Boeing 727-200	78,000	68.1			Medium	Large
McDonnell-Douglas MD-83	73,000	63.28			Medium	Large
Boeing 727-100[17]	72,500	62.4			Medium	Large
Boeing 727-100C[17]	72,500	62.4			Medium	Large
McDonnell-Douglas MD-90-30	71,000	64.41	2165	1520	Medium	Large
de Havilland Comet 4	70,700				Medium	Large
Boeing 737-700	70,000	58.06	1921	1415	Medium	Large
Airbus A320-100	68,000	66	1955	1490	Medium	Large
Boeing 737-400	68,000	54.9	2540	1540	Medium	Large
de Havilland Comet 3	68,000				Medium	Large
Boeing 377	67,000				Medium	Large
Boeing 737-600	66,000	54.66	1796	1340	Medium	Large
Airbus A220-300	65,000	57.61	1890	1494	Medium	Large
Hawker Siddeley Trident 2E	65,000				Medium	Large
Airbus A319	64,000	62.5	1850	1470	Medium	Large
Boeing 737-300	63,000	51.7	1939	1396	Medium	Large
Boeing 737-500	60,000	49.9	1832	1360	Medium	Large
Airbus A220-100	59,000	50.80	1463	1356	Medium	Large
Airbus A318[18]	59,000	57.5	1375	1340	Medium	Large
Boeing 717-200HGW	55,000	47.174	1950		Medium	Large
Douglas DC-7	55,000				Medium	Large
de Havilland Comet 2	54,000				Medium	Large
Boeing 717-200BGW	50,000	46.265	1950		Medium	Large
de Havilland Comet 1	50,000				Medium	Large
Douglas DC-6A	48,600				Medium	Large
Douglas DC-6B	48,500				Medium	Large
Embraer 190	48,000	43	2056	1323	Medium	Large
Caravelle III	46,000				Medium	Large
Fokker 100	46,000	39.95	1621	1350	Medium	Large
Douglas DC-6	44,000				Medium	Large
Avro RJ-85	42,000	36.74			Medium	Large
Handley Page Hermes	39,000				Medium	Large
Embraer 175	37,500	32.8	2244	1304	Medium	Large
Bombardier CRJ900	36,500	33.345	1778	1596	Medium	Large
Embraer 170	36,000	32.8	1644	1274	Medium	Large
Bombardier CRJ700	33,000	30.39	1564	1478	Medium	Large
Douglas DC-4	33,000				Medium	Large
Vickers Viscount 800	30,400				Medium	Large
Bombardier Q400	28,000	28.01	1219	1295	Medium	Large
Bombardier CRJ200	23,000	21.319	1918	1479	Medium	Large
ATR 72-600	22,800	22.35	1333	914	Medium	Large
Saab 2000	22,800	21.5	1300		Medium	Large
Embraer ERJ 145	22,000	19.3	2270	1380	Medium	Large
ATR 42-500	18,600	18.3	1165	1126	Medium	Small
Saab 340	13,150	12.930	1300	1030	Medium	Small
Embraer 120 Brasilia	11,500	11.25	1560	1380	Medium	Small
BAe Jetstream 41	10,890	10.570	1493	826	Medium	Small
Learjet 75	9,752	8.709	1353	811	Medium	Small
Pilatus PC-24	8,300	7.665	893	724	Medium	Small
Embraer Phenom 300	8,150	7.65	956	677	Medium	Small
Beechcraft 1900D	7,765	7.605	1036	853	Medium	Small
Cessna Citation CJ4	7,761	7.103	1039	896	Medium	Small
de Havilland Hercules	7,000				Medium	Small
Embraer Phenom 100	4,800	4.43	975	741	Light	Small

Reference: https://en.wikipedia.org/wiki/List_of_airliners_by_maximum_takeoff_weight

2. Difference between air speed and ground speed

Ground Speed

For a reference point picked on the ground, the aircraft moves relative to the reference point at the ground speed. Ground speed is also a vector quantity so a comparison of the ground speed to the wind speed must be done according to rules for vector comparison.

Airspeed

The important quantity in the generation of lift is the relative velocity between the object and the air, which is called the airspeed. Airspeed cannot be directly measured from a ground position, but must be computed from the ground speed and the wind speed. Airspeed is the vector difference between the ground speed and the wind speed.

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.

Reference: https://www.grc.nasa.gov/www/k-12/airplane/move.html

3.

Let us assume passenger commuter aircraft and large airliners. Aircraft move using their own engine power all the time on the airport apron and taxiways under their own power to go towards runways and after landing taxi to their assigned gate.

The only time they use external assistance is to pushback from the gate. Large turbofan aircraft need help to reverse via a pushback tractor. The engines are turned on after the pushback is complete and the aircraft can move forward under It’s own power.

To be accurate, some aircraft can reverse using a variable pitch prop or thrust reversing on turbofans but generally reversing is done via pushback tractors. Blasting jet reversers blows debris In the crowded gate area creating foreign object damage hazard for adjacent aircraft, gate equipment or terminal waiting area glass windows and also foreign particle entering the engine may leed to damage the engine so it is not recommended to use aircraft engine power to move it on the ground at Airport.

4.

• The pilot parks the aircraft in exactly the right place. Usually with the help of an automatic system, but occasionally guided by a marshaller waving two paddles or wands. Dozens of handling personnel are already standing by to perform a whole range of tasks simultaneously.

• As soon as the aircraft is stationary and the engines are switched off, the first priority is to disembark the passengers as quickly as possible. The apron handler places chocks in front of the wheels and connects the ground power. Meanwhile, the passenger bridge manoeuvres up to the door and a belt loader rolls up to the cargo hold. Luggage is unloaded and transferred to the terminal on baggage carts.
• Refuelling begins, usually from a hydrant at the stand. A hose is attached to this from a special vehicle called a dispenser, with the other side connected to the fuel tank in the wing.

• Now it is time to service the aircraft. The caterer loads new meals and takes away the food waste and used cutlery and crockery. Other activities include draining the lavatories, replacing the headrest covers, removing rubbish and distributing fresh blankets and in-flight magazine.
• A specialist team – or sometimes the crew themselves – cleans the cabin so that the new passengers board a pristine aircraft.
• Meanwhile, specialists from the airline conduct a technical check to make sure that the engines, wings, control surfaces, landing gear, instruments, doors and other equipment are in full working order.
• The aircraft is now ready for baggage to be loaded for the next flight. This is a quick process, on average taking only 10-15 minutes. A little later the passengers start boarding. As soon as they are all in their seats, the door is closed and the pilot informs air-traffic control that the flight is ready for departure.

• The apron handler removes the chocks. A so-called pushback truck reverses the aircraft into taxiing position, pushing it with a towbar attached to the nose-wheel strut. Or, in the most modern versions, by actually lifting the wheel. That speeds up coupling and decoupling.

• The aircraft taxis to the runway to depart at the agreed time.
• The pilot waits for permission to take off from air-traffic control. This is possible once the departure route is clear. As soon as the go-ahead is received, the plane takes to the air at full power.

5.

Take off power:

Power Requirement to Keep a Jet Aircraft in the Air.

The total energy of an aircraft flying in the atmosphere can be calculated using equation

E = 1/2mv^2+mgh

However, the engines mounted onto the wings of the plane are required to provide additional energy per time, power, in order to keep the aircraft flying at a constant altitude and speed. This extra power needed to overcome the drag acting on the airplane and is calculated using

P = (dh/dt)mg

where (dh/dt) is the decent speed required to keep the plane's speed constant if the engines fail.

Takeoff and Climb:

• When ready for takeoff, and cleared by Air Trafic Control to proceed, the pilot or first officer of an aircraft releases the brakes and advances the throttle to increase engine power to accelerate down the runway.Once aligned on the runway, steering the aircraft is normally accomplished by using foot pedals that manipulate the nose wheel until the speed is sufficient enough that wind rushing by the rudder on the aircraft tail makes nose wheel steering unnecessary.
• As the aircraft gains speed, air passes faster and faster over its wings and lift is created. Instruments onboard the aircraft display this airspeed, which equals not only the speed of the plane relative to the ground, but also the speed of any wind that may be blowing toward the aircraft (aircraft normally take off headed into the wind).
• When the airspeed reaches a certain predetermined point known as rotation speed, the pilot manipulates panels on the tail of the aircraft to rotate the nose of the plane upward. This creates even stronger lift and the plane leaves the ground.
• Rotation speed, abbreviated VR, is one of three important airspeed settings calculated before every flight .The others are V1 - the speed beyond which a safe stop on a runway is no longer possible; and V2 - the minimum speed needed to keep a plane flying should an engine fail after the aircraft surpasses V1. Some of the factors affecting VR and V2 are the weight of the aircraft, the air temperature and the altitude of the airport.
• The heavier the aircraft, the more lift, and thus speed is needed to get it off the ground. Aircraft also need to go faster to y on a hot day than on a cool day. Hot air is less dense than cool air and less density produces less lift for the same speed.
• Similarly, the higher the altitude, the less dense the air. Aircraft need more speed to leave the ground at a place like Denver than at a place like New York, with all other factors such as weight being equal. Some of these factors also are important in calculating V1, although the key factor is the length of the runway that is being used.
• Most large jets leave the ground at about 160 miles per hour and initially climb at an angle in excess of 15 degrees. The angle of a plane's wings to the air owing around them is extremely important to maintaining lift. If the so-called angle of attack is too severe, the ow of air around the wings becomes disrupted and the plane loses lift. To make an aircraft more aerodynamically effcient, the wheels on which an aircraft rolls when it is on the ground are retracted into a cavity in the belly of the plane after it is airborne. There is less drag (wind resistance), and an aircraft can fly faster when its landing gear is retracted.

Tyre design:

• 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 aeroplane needs to be distributed more evenly.
• A Boeing 737NG 737MAX uses 6 wheels, Boeing 787 uses 10 wheels, Boeing 777 uses 14 wheels and Airbus A380 uses 22 wheels. Aircraft tyres work under extreme conditions, carrying up to 340 tons and accelerating at over 250 km/hour at takeoff, in addition to enduring varied environmental stress when in flight and taxiing.

Design and Construction of Aircraft tyre:

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

1. They support the weight of an aircraft while it is on the ground.

2. It also provides the necessary traction for braking and stopping of an aeroplane.

3. Tyre also helps to absorb the shock of landing and provide cushioning the roughness of takeoff, roll-out, and taxi operations.

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 is operating at high speeds for a short time when required.

Some technical aspects of the tyre :

• 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 is the maximum permissible load at a specified inflation pressure.
• 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.
• The speed rating is the maximum takeoff speed to which the tyre has been tested.
• 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.
• Aircraft tyres may be Tube-type or Tubeless. Tubeless tyres are more advantageous over tube-type. There is no longer the use of tube-type tyre in recent aviation. Nowadays all airliners are using tubeless tyres. Tubeless that are meant to be used without a tube has the word TUBELESS on the sidewall of the tyre.
• Aircraft tyres may be Radial or Bias. Almost all airliners are using Radial tyre. Bias is an older design, and its mainly used for road vehicles. Radial tyres have the word RADIAL on the sidewall. Radial tires are more expensive than bias-ply tyres. Radial tires are in demand because of their lower life cycle cost and long term value.

This is the Construction of Radial tyre.

Rolling resistance :

Rolling resistance is one of the forces that act to oppose the motion of a cyclist. It is caused mainly because of deformation of the tyre and can be understood by thinking about

• energy losses due to heat (hysteresis)
• the forces pushing on the tyre.

Energy is lost as heat As the tyre comes into contact with the road, it changes shape as it is compressed (pushed in a bit). This compression causes parts of the rubber tube and the casing of the tyre to heat up. It also causes the tread on the outside of the tyre to heat up as it comes into contact with the road. A tyre with knobbly tread will have a lot more rolling resistance than a smooth tyre because there will be more rubber being compressed and so there will be more heat.

The tyre is a bit like a spring or a rubber band. Some of the energy is stored as the tyre becomes compressed (squeezed in). As the tyre comes back off the road, there is not as much of this stored energy returned because some of it has gone towards making the tyre heat up. This loss of available energy due to heating is called hysteresis. This means there will be less energy available to make the bike go faster.

If you feel the temperature of your tyres when you have been biking fast, you will notice this heat. If your tyres are not pumped up hard, there will be even more heat created.The force of rolling resistance does not change at higher speeds. However, because there is a lot more heat being produced at higher speeds, the cyclist uses more power (energy per second) to work against rolling resistance.

Tyre pressure:

An aircraft tire or tyre is designed to withstand extremely heavy loads for short durations.The number of tires required for aircraft increases with the weight of the aircraft, as the weight of the airplane needs to be distributed more evenly. Aircraft tire tread patterns are designed to facilitate stability in high crosswind conditions, to channel water away to prevent hydroplaning, and for braking effect.

Aircraft tires also include fusible plugs (which are assembled on the inside of the wheels), designed to melt at a certain temperature. Tires often overheat if maximum braking is applied during an aborted takeoff or an emergency landing. The fuses provide a safer failure mode that prevents tire explosions by deflating in a controlled manner, thus minimizing damage to aircraft and objects in the surrounding environment.

Inflation : Each of the twelve Boeing 777-300ER 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) and is changed every 300 cycles while the brakes are changed every 2000 cycles.Aircraft tires generally operate at high pressures, Inflation up to 200 psi (14 bar; 1,400 kPa) for airliners, and even higher for business jets.Tests of airliner aircraft tires have shown that they are able to sustain pressures of maximum 800 psi (55 bar; 5,500 kPa) before bursting.Aircraft tires are usually inflated with nitrogen to minimize expansion and contraction from extreme changes in ambient temperature and pressure experienced during flight.

Brake forces and landing:

Bringing at aircraft down to the runway from 37,000 feet is only part of the challenge. Its not over until the aircraft is safely parked at its gate. In order to do this, pilots have a number of systems available to slow the aircraft down, even in a blizzard on a snowcovered runway.

The 787 braking system: Stopping a 200-tonne aircraft landing at 180 mph requires a lot of braking force. To do this, the 787 has one brake unit on each of the eight wheels on the main gear assembly.On other aircraft types, the brake units are powered by the hydraulics system. An electrical signal is sent from the flight deck to hydraulic actuators near the main landing gear. Here, hydraulic fluid at 3,000 pound per square inch is used to force the brake unit against the wheel, thus slowing it down.Thats the case on the 787 Dreamliner. Designers did away with the use of the hydraulic system and all its associated architecture and instead used electricity to power the brakes. When the pilots press on the brake pedals, an electrical signal is sent to the brake unit on the wheel. Here, electrically powered actuators are used to press the carbon brake disc against the wheel, slowing it down.

Electric brakes The brake system on the 787 Dreamliner is controlled by the pilots pressing the tops of the rudder pedals under their feet, demanding the rate of braking which they require. This sends an electronic signal to the Left and Right Brake System Control Units.These then send signals to the four Electronic Brake Actuator Controllers (EBAC) which control the rate of braking on the wheels. Each wheel has four Electric Brake Actuators (EBA), a kind of piston which presses against the carbon brake discs.

The brake disks themselves are made up of two parts. Firstly, there are the rotors. These are connected to the wheel by drive tabs (in the video below they are the black rectangles on the rotor disks). As these drive tabs are in contact with the inside of the wheel, they spin at the same speed. Depending on the brake manufacturer, there are either four or five of these rotors on each brake assembly.The second part of the disks are the stators. These sit around each rotor and are fixed in place and thus dont move. As the wheel turns, the rotors spin round inside the stators.

When the brakes are applied, the four EBAs apply pressure to the first stator. This in turn squeezes the stationary stators up against the spinning rotors and its this friction which slows the wheel down.

Anti-skid protection When landing on slippery runways, theres a chance that the wheels may start to skid as the brakes are applied. To stop this from happening and to maintain maximum effective braking, each wheel has anti-skid protection.Using a variety of sources to determine the aircraft speed, the brake units know how fast the wheels should be spinning. If that speed drops significantly, its because the current brake pressure on that wheel is too great and the wheel is just skidding over the surface.

In this situation, the anti-skid system automatically reduces the braking on that wheel to a point where the skid stops before reapplying the pressure. All this is done in a fraction of a second.

Bottom line Bringing an aircraft to a safe stop is the most important part of a flight. In order to do this, pilots have a number of facilities available to them.The brakes bear the brunt of the hard work with the spoilers and reverse thrust lending a helping hand to ensure maximum efficiency. The autobrake system helps keep the deceleration nice and smooth whilst the anti-skid system reduces the distances needed to stop by modulating the brakes on individual wheels and stopping them from skidding.

Aircraft can also depart with part of the braking system not working. By carrying out a performance calculation before every takeoff and landing, we ensure that the aircraft will stop safely in the given conditions, even at maximum takeoff weight.

6.

A. Power required to pull/push ariplane with towing vehicle

Assuming the average parameter of an airplane

Total mass of airplane(including payload) = 575,000kg

mass of push back = 1000kg

Rolling resistence(Frr)

coefficient of rolling resistence =Crr = 0.002

Rolling resistence force = Frr = Crr*m*g

For air craft Frr = 0.002*575000*9.81 = 11281.5 N

For towing vehicle Frrt = 0.002*1000*9.81 = 19.62N

Aerodynamic drag force

Drag coefficient Cd = 0.025

air density (ρ)= 1.125kg/m^3

frontal area (A) = 150`m^2`

velocity (V) = 14.5kmph

Far = 1/2Cd * ρ*A*V^2

= 1/2 *0.025*1.125*150*(4)^2 = 33.75N

Hill climb force

Fh = mgsinθ

Runways are constructed flat so the hill climg force can be neglected

Total resistence

Ft = 11.2815KN

Power required

P = Ft*v

= 11.2815*4 = 45.26KW

The minimum power required by the towing vehicle is 45.26KW to pull/push the Airplane at 4m/s

B. The simulink model to calculate the above conditions

7.

A. Parameter assumed for designing the electric power train block of motor

Sl no.	Assumed parameter	Assumed values
1	Mass of aircraft	575000kg
2	Mass of towing vehicle	1000kg
3	Rolling resistence coefficient of aircraft	0.002
4	Rolling resistence coefficient of towing vehicle	0.002
5	Velocity of aircraft while towing	4m/s
6	Density of air (ρ)	1.125kg/m^3
7	Frontal area of aircraft	150m^2
8	Time for towing	15mins
9	Tyre radius	25 inch
10	Overall gear ratio	8
11	Transmission efficiency	85%
12	Motor efficiency	95%

Based on the calculation done above

force required = 11.2815KN

Required power = 45.26KW

assuming the tyre radius as 25 inch = 0.635m

Torque required at wheel = (Total force)*Radius = 7.16KNm

Motor torque = Wheel torque/(Gear ratio * Efficiency) ..........Assuming gear ratio as 8 and transmition efficiency as 85%

7.16/8*0.85 = 1.052KNm

If the motor is considered to be 95% efficient then Motor torque = 1.052/0.95 = 1.107KNm

Similarly power required by motor considering all efficiency = 45.26/0.85*0.95 = 56.04Kw

Let us assume the towing activity takes for 15mins = 0.25Hr

total energy consumed = 56.04*0.25 = 14.01Kwh

A battery of higher capacity than this has to be selected.

If the battery of 150Kw power rating is selected the duty cycle range to control the speed from 0 to max (here 4m/s) is

d = Required power/Rated power = 56.04/150 = 0.3736

This means the controller should provide the duty cycle ranging from 0 to 37.36% in order to control the towing speed.

Block diagram of Power train of Towing machine

B.