Sample Loading Problem(B407)[PDF]

Introduction

This document presents an example weight and balance calculation for the Bell 407 helicopter.

Performance data are taken from the Bell 407 Rotorcraft Flight Manual (BHT-407-FM-1).

Practical Example

Conditions and Objectives

Helicopter: Bell 407

Empty Weight(lbs): 3050, Longitude CG(In): 131, Latitude CG(In):0.1

Oil(lbs): 13, Longitude CG(In): 205, Latitude CG(In):0.0

Loading:

  • 1 Pilot
  • 4 Passengers (1 Front seat, 1 Mid-Passenger left seat, 2 Aft-Passenger left/right seat)
  • Baggage(lbs): 150
  • Take-off Fuel(lbs): 700 (JP-5)
  • Trip Fuel(lbs): 550 (JP-5)

Objectives:

  1. Find the Take-Off Gross Weight and CG.
  2. Find the most forward CG condition.
  3. Find the most aft CG condition.
  4. Find the Landing Gross Weight and CG.
  5. Check the longitudinal CG limits.
  6. Check the lateral CG limits.

Interpolation

Performance data provided in tables are always shown as round values to simplify the calculations. Pilots have two ways to deal with it: use the next higher number or simply the closest number to make quick calculations and optionally provide for extra margin. Sometimes it is also reasonable to interpolate between two near numbers.

Interpolation formula.jpg

where
X – input variable ;
Xlow – lowest value of two in table ;
Xhigh – highest value of two in table ;
Flow – lowest corresponding to X value in table ;
Fhigh – highest corresponding to X value in table.

If this is not so clear, do not worry; several examples are present below.

We will roll down some results to “worse” numbers to avoid long calculations within this document.

Take-Off Gross Weight and CG

Empty Weight and Oil

1. Calculate longitudinal moment of empty weight.
  • Empty Weight(lbs): 3050
  • Longitude CG(In) : 131.0

CodeCogsEqn-7.gif

2. Calculate lateral moment of empty weight.
  • Latitude CG(In):0.1

CodeCogsEqn-31.gif

3. Calculate longitudinal moment of oil.
  • Oil(lbs): 13
  • Longitude CG(In): 205

CodeCogsEqn-32.gif

4. Calculate lateral moment of oil.
  • Latitude CG(In):0.0

CodeCogsEqn-8.gif

5. Now create a Table of Results.
Longtitude Latitude
Weight CG Moment CG Moment
Weight Empty 3050.0 131.0 399559.0 0.1 305.0
Oil 13.0 205.0 2665.0 0.0 0

Crew, Passengers and Cargo

Go to Cabin and Baggage Compartment Table of Moments Inch-Pounds.

6. Find longitudinal moment of the Pilot.

Cabin and Baggage Compartment table of Moments.png

This table provides moment values according to the weight and seat of the crew/passenger. We will use a standard value of 200lbs for each crew member and passengers on board.

If the actual weight of the passengers are not known, standard weights can be used. These values are determined by statistical surveys and varies slightly between regions.
Standard weights should not be used for aircraft having less than 7 seats.

Go to the Buttock Lines Inches table.

7. Find the lateral CG of the pilot and calculate his/her moment.

Buttock Lines Inches.png

This chart provides lateral station values for each crew/passenger seat.

CodeCogsEqn-9.gif

8. Update the Table of Results.
Longtitude Latitude
Weight CG Moment CG Moment
Weight Empty 3050.0 131.0 399559 0.1 305
Oil 13.0 205.0 2665 0.0 0
Pilot 200.0 65.0 13000 14.0 2800

Go to Cabin and Baggage Compartment Table of Moments Inch-Pounds.

9. Find longitudinal moments of Passengers and Baggage.

Cabin and Baggage Compartment Table of Moments.png

Go to the Buttock Lines Inches table.

10. Calculate lateral moments of the Passengers and Baggage.

Buttock Lines Inches2.png

CodeCogsEqn-10.gif

CodeCogsEqn-11.gif

CodeCogsEqn-12.gif

CodeCogsEqn-14.gif

CodeCogsEqn-15.gif

11. Calculate longitudinal and lateral CG at Zero Fuel Weight.

CodeCogsEqn-50.gif

12. Update the Table of Results.
Longtitude Latitude
Weight CG Moment CG Moment
Weight Empty 3050.0 131.0 399559 0.1 305
+Oil 13.0 205.0 2665 0.0 0
+Pilot 200.0 65.0 13000 14.0 2800
+Forward Passenger 200.0 65.0 13000 -11.1 -2220
+Mid Passenger 200.0 91.0 18200 -13.0 -2600
+Aft Passanger(1) 200.0 129.0 25800 -16.8 -3360
+Aft Passanger(2) 200.0 129.0 25800 16.8 3360
+Baggage 150.0 174.0 26100 0.0 0
Gross Weight at Zero Fuel 4213.0 124.4 524124 -0.4 -1715

Fuel

Go to the Fuel Loading Table

13. Find the weight, longitudinal CG and moment of take-off fuel.

Fuel loading Table-1.png

Our fuel on board is 700lbs and no pre-calculated values are available for 700lbs of fuel in our table. This means that we have to calculate it by ourself via interpolating or selecting the next higher number as explained above.

For this situation we will use interpolation.

CodeCogsEqn62.gif

14. Calculate longitudinal and lateral CG at Take-off Gross Weight.

CodeCogsEqn-48.gif

15. Create a new Table of Results for take-off Gross Weight.
Longtitude Latitude
Weight CG Moment CG Moment
Gross Weight at Zero Fuel 4213.0 124.4 524124 -0.4 -1715
+Take off Fuel (JP-5) 700.0 122.9 86072 0.0 0
Take-off Gross Weight 4913.0 124.2 610196 -0.35 -1715

Most Forward and Aft CG Conditions

16. Find the weight, longitudinal CG and moment of fuel at most forward CG condition.

Fuel loading MF.png

17. Calculate longitudinal and lateral CG at most forward CG condition.

CodeCogsEqn-46.gif

18. Create a new Table of Results for most forward CG condition.
Longtitude Latitude
Weight CG Moment CG Moment
Gross Weight at Zero Fuel 4213.0 124.4 524124 -0.4 -1715
+Critical Fuel for Most Forward 508.6 116.9 58998 0.0 0
Most Forward CG Condition 4721.6 123.5 583122 -0.36 -1715
19. Find the weight, longitudinal CG and moment of fuel at most aft CG condition.

Fuel Loading MA.png

20. Calculate longitudinal and lateral CG at most aft CG condition.

CodeCogsEqn-47.gif

21. Create a new Table of Results for most aft CG condition.
Longtitude Latitude
Weight CG Moment CG Moment
Gross Weight at Zero Fuel 4213.0 124.4 524124 -0.4 -1715
+Critical Fuel for Most Aft 193.1 137.0 26455 0.0 0
Most Aft CG Condition 4406.1 124.96 550579 -0.39 -1715


Landing Gross Weight and CG

21. Find the weight, longitudinal CG and moment of landing fuel.

First we will calculate the landing fuel.

CodeCogsEqn-53.gif

Fuel loading lw.png

Now we will make interpolations to calculate exact values of CG and moment.

CodeCogsEqn-54.gif

22. Calculate longitudinal and lateral CG at landing gross weight.

CodeCogsEqn-56.gif

23. Create a new Table of Results for landing Gross Weight.
Longtitude Latitude
Weight CG Moment CG Moment
Gross Weight at Zero Fuel 4213.0 124.4 524124 -0.4 -1715
+Landing Fuel (JP-5) 150 136.5 20480 0.0 0
Landing Gross Weight 4363.0 124.82 544594 -0.39 -1715


24. Combine all the tables you have created.
Longtitude Latitude
Weight CG Moment CG Moment
Weight Empty 3050.0 131.0 399559 0.1 305
+Oil 13.0 205.0 2665 0.0 0
+Pilot 200.0 65.0 13000 14.0 2800
+Forward Passenger 200.0 65.0 13000 -11.1 -2220
+Mid Passenger 200.0 91.0 18200 -13.0 -2600
+Aft Passenger(1) 200.0 129.0 25800 -16.8 -3360
+Aft Passenger(2) 200.0 129.0 25800 16.8 3360
+Baggage 150.0 174.0 26100 0.0 0
Gross Weight at Zero Fuel 4213.0 124.4 524124 -0.4 -1715
+Take off Fuel (JP-5) 700.0 122.9 86072 0.0 0
Take-off Gross Weight 4913.0 124.2 610196 -0.35 -1715
Gross Weight at Zero Fuel 4213.0 124.4 524124 -0.4 -1715
+Critical Fuel for Most Forward 508.6 116.9 58998 0.0 0
Most Forward CG Condition 4721.6 123.5 583122 -0.36 -1715
Gross Weight at Zero Fuel 4213.0 124.4 524124 -0.4 -1715
+Critical Fuel for Most Aft 193.1 137.0 26455 0.0 0
Most Aft CG Condition 4406.1 124.96 550579 -0.39 -1715
Gross Weight at Zero Fuel 4213.0 124.4 524124 -0.4 -1715
+Landing Fuel (JP-5) 150 136.5 20480 0.0 0
Landing Gross Weight 4363.0 124.82 544594 -0.39 -1715

Check the CG Limits

Go to the Longitudinal C.G. Table

25. Check longitudinal CG positions for take-off GW, fuel at most forward CG, fuel at most aft CG and landing gross weight.

Longdititunal CG.png

Now we will draw individual arrows from corresponding points of total moment and fuselage stations to find the longitudinal CG points for take-off GW, fuel at most forward CG, fuel at most aft CG and landing gross weight.

According to this table we confirm that the collective CG of our load is within longitudinal CG limits.

Go to the Lateral C.G. Table

26. Check lateral CG positions for take-off GW, fuel at most forward CG, fuel at most aft CG and landing gross weight.

Lateral CG.png

We will again draw individual arrows from corresponding points of total moment and fuselage stations to find the lateral CG points for take-off GW, fuel at most forward CG, fuel at most aft CG and landing gross weight.

According to this table we confirm that the collective CG of our load is within lateral CG limits.

See also

Reference

  • None

Author

  • VID 522050 - Creation

DATE OF SUBMISSION

  • 12:42, 23 February 2021

COPYRIGHT

  • This documentation is copyrighted as part of the intellectual property of the International Virtual Aviation Organisation.

DISCLAIMER

  • The content of this documentation is intended for aviation simulation only and must not be used for real aviation operations.


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