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:
- Find the Take-Off Gross Weight and CG.
- Find the most forward CG condition.
- Find the most aft CG condition.
- Find the Landing Gross Weight and CG.
- Check the longitudinal CG limits.
- 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.
where
X – input variable ;
X_{low} – lowest value of two in table ;
X_{high} – highest value of two in table ;
F_{low} – lowest corresponding to X value in table ;
F_{high} – highest corresponding to X value in table.
If this is not so clear, do not worry; several examples are present below.
Take-Off Gross Weight and CG
Empty Weight and Oil
- Empty Weight(lbs): 3050
- Longitude CG(In) : 131.0
- Latitude CG(In):0.1
- Oil(lbs): 13
- Longitude CG(In): 205
- Latitude CG(In):0.0
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.
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.
Go to the Buttock Lines Inches table.
This chart provides lateral station values for each crew/passenger seat.
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.
Go to the Buttock Lines Inches table.
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
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.
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
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 |
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
First we will calculate the landing fuel.
Now we will make interpolations to calculate exact values of CG and moment.
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 |
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
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
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.