Payload Calculations For CPL/ ATPL 2


PAYLOAD CALCULATIONS

 

For PAYLOAD CALCULATIONS in aviation one first needs to understand certain terminologies that are used frequently.

Payload.  It is the load which can be carried in the form of passengers and cargo.

Manufacturers Empty Weight.   The weight of the structure, power plant, furnishings, systems and other items of equipment that are considered an integral part of the aircraft. It is essentially a dry weight, including only those fluids contained in closed systems (E.g. Hydraulic fluid).

Usable Fuel.   Fuel available for flight planning. This is lesser than the fuel carried on board (FOB).

Unusable Fuel.   Fuel remaining in the tanks after a run out test has been completed in accordance with regulations. UNUSABLE FUEL IS GENERALLY A RESULT OF THE DESIGN AND LOCATION OF THE WING TANKS.

FOB- UNUSABLE FUEL = USABLE FUEL

 Operational Empty Weight.   The manufacturers empty weight plus the operators items, i.e. the flight crew, cabin crew and their baggage, unusable fuel, engine oil, emergency equipment, toilet chemicals and fluids, gallery structure, catering equipment, seats, documents, etc.

OEW = MEW + (CREW, BASIC FURNISHING, OILS, EMERGENCY EQPT…)

Dry Operating Weight.   The total weight of an aircraft ready for specific type of operation excluding all usable fuel and traffic load. Operational empty weight plus items specific to type of flight, i.e. catering, newspapers, pantry equipment, etc..

Also called APS – Aircraft Prepared For Service Weight

If Fuel is added aircraft is ready to go

Addition of passengers and load/freight would earn revenue

Useful Load.   The difference between Gross Take Off Weight and Dry Operating Weight. In other words , it is all the load which is removable, which is not essentially required to operate the airplane.

It includes : Passengers + Baggage/ Freight, etc

Payload.  The load available as passengers, Baggage, Freight etc. This is the part of Gross Weight that earns revenue for the airline

USABLE FUEL =  TRIP FUEL + RESERVE FUEL

 Gross Take Off Weight.   The weight of the aircraft loaded for Take Off. It includes the APS Weight plus the Useful Load plus FOB. This is the actual weight at the time of Take Off.

 GROSS TAKE OFF WEIGHT = DRY OPERATING WEIGHT + USEFUL LOAD + FOB  

  Aim of Payload Calculations

To maximize payload and in turn maximize revenue, while maintaining safety in terms of fuel planning which would include adequate reserves, performance safety and still not exceed stipulated weight limits

Gross Take Off Weight Limits.   Weight limits for take off arises from three conditions:

Take Off weight Limits

Zero Fuel Weight limits

Landing Weight Limits

The most restricting payload value that emerges from these three abovementioned considerations is the payload that one can Take Off with, in other words Maximum Take Off Weight Limit.

 

PAYLOAD CALCULATIONS

AICRAFT AUW BREAKDOWN

 

FOB (FLT FUEL +RESERVE)

 

TAKE OFF WT (TOW)

 

PAYLOAD (PAX + CARGO)

 

ZERO FUEL WT (ZFW)
NEWS PAPER + CATERING

 

DRY OPERATING WT

 

CREW + BAGGAGE

 

BASIC WT OR APS WT

 

AIRFRAME + ENGINE + AVIONICS

 

MANUFACTURERS EMPTY WT (MEW)

MTOW (Maximum Take Off Weight).   It is the Take Off weight given by the manufacturer which cannot be exceeded in any circumstances.  This caters for the best operating conditions i.e. runway length, elevation, density altitude, runway gradient, runway condition and winds etc.  It is also known as Max Gross take off wt.

MTOW is a design limitation for the maximum Take Off Weight and is listed in the Aircraft Manual. Under no circumstances can actual Take Off Weight exceed the MTOW.

RTOW.    (Restricted/regulated/rated Take Off Weight)  This is the take off weight restricted due to prevailing conditions at the places of departure. In other words the Take Off weight that is arrived at in accordancewith regulations governing aircraft performance is called the Regulated Take Off Weight.

Now, under no circumstance can:

Actual Weight exceed RTOW and

RTOW exceed MTOW

Actual Take Off Weight (ATOW) < RTOW < MTOW

Therefore, Max value of Payload can be obtained fron the formula

APS Wt + FOB + Payload = RTOW

In case RTOW is not given in the question then

APS Wt + FOB + Payload = MTOW

TOW  = BASIC WT + PAYLOAD + FUEL ON BOARD (FOB)

          PAY LOAD = TOW – (BASIC WT + FOB)    

 Payload Limitations due to Maximum Zero Fuel Weight Considerations     

 MZFW (Max Zero Fuel Wt).  Bending moments, which the wing is subjected to is maximum when the wing tanks is minimum. During flight, the quantity of fuel in the wings reduce. As a result, it is necessary to limit the weight when there is no fuel in the tanks. When wing tanks are empty there is a maximum permissible weight of an aircraft including all its contents.  Exceeding this weight causes unacceptable load to the structure of the aircraft.  Above this weight, if any load is taken onboard it can be fuel only. This weight is called the Maximum Zero Fuel Weight. This weight is specified in the manual.

        MZFW = PAYLOAD + BASIC WT(APS Weight)

 Payload Limitations due to Maximum Landing Weight

MLW (Max Landing Wt)  It is the maximum weight at which a landing can be made at a destination without imposing any structural damage to the aircraft. The Landing Weight is limited, assuming a landing impact with a vertical speed of – 3.05 m/s (- 600 Ft/Min). This is a design and structural limit and is again listed in the manual.

MLW = APS or Basic Weight = Fuel in tanks when Landing + Payload

 Determination of final value of Payload that can be carried

The 3 equations can be combined and listed together. Each equation provides one value of Payload and can be written as PL1, Pl2 and PL3

APS Wt + FOB + PL1 = RTOW or MTOW

APS Wt + PL2 = MZFW

APS Wt + Fuel in Tanks at Landing + PL3 = MLW

 Certain Figures to know before solving problems

FOB ( Fuel at Take off point)  =  Ramp Fuel – Taxi Fuel

Take Off Mass                           =  Apron Wt – Taxi Fuel

Flight or Trip Fuel                   =  Fuel on Board – Reserve Fuel

 

 Numericals on Payload.   To solving any problem on Payload the following procedure is adopted:-

Step 1.   Make a table as given below and enter relevant information as given in the problem:-

MTOW RTOW MLW + Flight Fuel MZFW + FOB

Choose the lowest value obtained out of MTOW/RTOW/MLW OR MZFW. Then calculate Payload by substituting this value of TOW in Payload = MTOW – (BASIC WT + FOB)

Q.    MTOW = 83000 lbs, MLW = 66000 lbs, Basic Wt = 52000, FF = 20000 lbs, Reserve = 2800 lbs. Find Payload.

 

MTOW RTOW MLW + Flight Fuel MZFW + FOB
83000* 66000 + (20000- 2800) = 83200

* LOWEST VALUE

PAYLOAD = TOW – (BASIC WT + FOB) = 83000 – (52000 + 20000) = 11000 lbs

 

Q.    MTOW = 82000 lbs, MLW = 64500 lbs, Basic Wt = 50000, FOB = 20000 lbs, Reserve = 4000 lbs. Find Payload.

 

MTOW RTOW MLW + Flight Fuel= TOW MZFW + FOB = TOW
82000 64500 + (20000- 4000) = 80500*

* LOWEST VALUE

PAYLOAD = TOW – (BASIC WT + FOB) = 80500-(50000 + 20000) = 10500 lbs

 Q.   In the above question can you carry additional fuel without affecting payload?

Ans.   Yes, (82000-80500=1500) but the fuel carried has to be consumed (burn off/dump) prior to landing,

 Q.    MTOW = 120000 lbs, MLW = 90000 lbs, MZFW = 85000, Basic Wt = 76400, Trip Fuel = 15000, Reserve = 2000 lbs. Find Payload.

 

MTOW RTOW MLW + Flight Fuel= TOW MZFW + FOB = TOW
120000 90000 + (15000) = 105000 85000 + 17000 = 102000*

* LOWEST VALUE

PAYLOAD = TOW – (BASIC WT + FOB) = 102000 – (76400 + 17000) = 8600 lbs

 Q.   In the above question find payload if Flight Fuel is reduced by 1000 lbs and increased by same amount?

Ans.   Payload in both cases will remain the same since value of MZFW has been applied.

 

Q.   MTOW = 20000 lbs, MLW = 18000 lbs, MZFW = 17000, Basic Wt = 14000, Trip Fuel = 3000, Reserve = 1600 lbs Find (a) Payload (b) Payload if aircraft consumed 700 lbs reserve before landing  (c)  Find Payload if FOB is reduced by 700 lbs.

 

MTOW RTOW MLW + Flight Fuel= TOW MZFW + FOB = TOW
20000* 18000+ 3000 = 21000 17000 + 4600 = 21600

* LOWEST VALUE

PAYLOAD = TOW – (BASIC WT + FOB) = 20000 – (14000 + 4600) = 1400 lbs

(b)  Will remain same   (c) Payload can be increased by 700 lbs (1400+700) =2100

 

Q.   Fuel Consumption = 120 lbs/hr; MTOW = 7150 lbs, MLW = 6900 lbs, MZFW = 6150 lbs, Basic Wt = 5000 lbs, Reserve = 120. Dist =960 Nm, TAS=180k, Head Winds of 20 Kts. Find payload in NIL wind conditions.

Ans.   Dist = 960 nm; TAS = 180 Kts, Time = 5.33, FF = (5.33 x 120 lbs/hr) = 640 lbs.

 

MTOW RTOW MLW + Flight Fuel= TOW MZFW + FOB = TOW
7150 6900+640 = 7540 6150 + 800 = 6950*

* LOWEST VALUE

PAYLOAD = MTOW – (BASIC WT + FOB) = 6950 – (5000 + 800) = 1150 lbs

 

Q.   A flight is to be made from M to N and return to M carrying max payload in each direction. Fuel is not available at N. Distance M to N =80 Nm, Mean GS M to N = 70 kts, Mean GS N to M = 110 Kts, Mean Fuel consumption = 410 Kg/hr, MTOW at M = 6180 kg, MLW at M = 5740 kg MTOW at N = 5800 kg, MLW at M = 5460 kg, MZFW = 5180, Basic Wt = 4400 kgs, Res Fuel = 250 kgs.  Calculate (a) Max payload which can be carried from M to N and from N to M.

Ans.   Total Fuel = Fuel reqd from M to N + Fuel reqd from N to M + Reserve

Fuel reqd: M to N = 80/70 x 410 = 1.42 x 410 = 468,

Fuel reqd: N to M = 80/110 x 410 = 0 .727 x 410 = 298,

FF = 468 + 298 = 766 kgs, Reserve = 250 kgs, Total Fuel = 1016 Kgs.

Payload from M to N:

 

MTOW RTOW MLW + Flight Fuel= TOW MZFW + FOB = TOW
6180* 5740 +468 = 6208 5180 + 1016 = 6196

* LOWEST VALUE

PAYLOAD = MTOW – (BASIC WT + FOB) = 6180 – (4400 + 1016) = 764 kgs

Payload from N to M:

 

MTOW RTOW MLW + Flight Fuel= TOW MZFW + FOB = TOW
5800 5460+298 = 5758 5180+(1016- 468) = 5728*

* LOWEST VALUE

PAYLOAD = MTOW – (BASIC WT + FOB) = 5728 – (4400 + 548) = 780 kgs

 

Q.   Given MTOW = 34,500 kgs, MZFW = 28,000, MLW = 31,000, Empty Wt = 17,500 kgs, TAS = 350 Kts, Fuel Consumption = 1450 Kg/hr. Reserve Fuel 1200 kgs for all flghts (assume not used) Fuel Tank Capacity = 10, 500 kgs. Find (a) Max Payload   (b) In NIL wind condition distance upto which above payload can be carried.  (c) Max distance you can fly in NIL winds.  (d)  What payload you can carry in  part (c).

Ans.  

Max payload = MZFW – Basic Wt = 28000-17500 = 10500 kgs.

TOW =10500 + 17500 +FOB or 34500=28000 + FOB

FOB = 6500.  Hence FF = 6500-1200 = 5300 kgs.

Fuel Flow = 1450 kg/hr,

TAS = 350 hence max distance = 5300/1450 x 350 = 1279 Nm.

Tank capacity = 10500 kgs.

Hence 10500 – 6500 = 4000 kgs of fuel can be carried in lieu of payload.

So total fuel available = 5300 + 4000 = 9300 kgs.

Hence max distance = 9300/1450 x 350 = 2245 Nm and pay load would reduce by 4000 kgs in lieu of fuel.

Payload = 10500-4000 = 6500 kgs.

PAYLOAD CALCULATIONS

Payload

 

 

 

 

 

 

 

 

 



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