Mass and Balance

NOTE: ALL GRAPHS AND TABLES ARE FOR DEMONSTRATION PURPOSES AND ARE NOT TO BE USED FOR ACTUAL CALCULATIONS.

Refer to the approved POH for your aircraft for actual use.

Recap:

When loading an aircraft there are a number of considerations:

1) Weight  (MAUW) Maximum All Up Weight. (MTOW) Maximum Take Off Weight.

2) C of G Location of the Centre of Gravity.

3) WAT Weight and Temperature Limitations.

1) Weight:

The performance of an aircraft is profoundly affected by excessive weight.

a) Higher Take Of speed.

b) Longer Take Off Run.

c) Longer Take Off Distance to clear a 50ft obstacle.

d) Reduced climb performance.

e) Greater fuel consumption.

f) Reduced Range.

g) Higher stalling speed.

h) Higher landing speed.

i) Longer landing roll.

The maximum amount of weight an aircraft can carry is a structural and performance limitation and will clearly be indicated in the POH.

For most light aircraft Maximum All Up Weight (MAUW) and Maximum Take Off Weight (MTOW) are the same. On more complex and larger aircraft there are many other considerations which must be understood and referred to in the POH of the particular aircraft.

2) Centre of Gravity:

How an aircraft is loaded and where the weight is placed is vitally important and if not enough care is taken the stability and controllability of an aircraft can be severely affected.

An aircraft loaded with the C of G too far aft will cause a nose up pitching moment and if too far aft may even cause the aircraft to be completely uncontrollable leading it into a stalling attitude at low speeds such as just after take off. It can also present difficulties during landing.

An Aft C of G can make stall and spin recovery difficult and sometimes impossible depending on the aircraft type and severity of misplacement of the C of G.

If the C of G is too far forward it will cause the aircraft to be nose heavy and make it difficult for the pilot to rotate during take off and can also present control difficulties during the climb and landing phases of flight.

Should a stall occur, a lot of height may be lost before a full recovery is made.

3) WAT: (Weight and Temperature Limitations)

By no means can it be assumed that if the MAUW and C of G are in limits that a safe take off and clearance of obstacles can be achieved.

To determine this, careful calculations must be made in terms of surface temperatures and pressure altitudes at the airfield from which a departure is anticipated. As we have learnt high density altitudes can severely impede an aircrafts performance.

For this we must consult the POH in order to establish the maximum weight an aircraft can be loaded to in order to achieve safe Take Off Performance and then subsequent required Climb Performance.

RECAP BALANCE

a)  C of G

The Centre of Gravity is the point at which if suspended or placed on a fulcrum, the aircraft would balance, neither pitching nose down, or tail down.

mb_1

b)  Reference Point or Datum.

To simplify matters aircraft manufacturers provide a reference point or datum from which all measurements of balance are taken. This point is usually expressed in inches forward of the leading edge of the wing or some other suitable point such as the firewall. See the example below where the datum is 79.6 inches forward of the leading edge of the wing.

mb_2

c) Arm.

The Arm is the horizontal distance from the Datum at which a load will be placed in an aircraft, for example the baggage compartment, the pilot and passenger seats, fuel tanks etc.

The Arm is usually expressed in inches. Some aircraft manuals state the Arm as a Flight Station (FS). An Arm of say 40 inches is the same as FS 40.

d) Moment.

The moment is the product of the Weight of an item multiplied by it’s Arm.

Weight x Arm = Moment.

In most light aircraft Weight is expressed in Lbs and Arm is expressed in Inches. The resultant Arm is therefore expressed as Inch/pounds

Example: 350 Lbs (W) X 80 Inches (A) = 28,000 MOMENT.

A Reduction Factor is often used to make these figures easier to work with, example Moment/1000 which then reduces a moment of say 511,220.33 to a more convenient figure of 511.22.

e) Principles involved. (Balance)

The effect of a 100 lb weight placed 20 inches from a fulcrum or datum is shown below

i.e. a Moment of 2000 in/lbs.

mb_3

  

 To balance this, an equal force must be placed on the opposite side of the fulcrum

mb_4

In the following example balance is achieved by placing a weight twice that of 100 lbs i.e. 200 lbs on an arm half the length (10 inches) which produces an equal moment of 2000 lb/inches.

mb_5

Now let’s see how we can apply this theory to the completion of a Load-sheet.

Simply put it is the pilot in commands legal responsibility to ensure that the aircraft is loaded such that:

a) The Maximum Take Off  Weight is not exceeded.

b) The aircraft is loaded within the C of G limits.

c) That all considerations in terms of WAT are met and that a safe take off and departure can be made from the departure runway.

EXERCISE

FIRST We need the Mass & Balance details of the specific aircraft. These Details will be shown in the CAA approved Mass and Balance Report. (See Aircraft documents)

We will also need to have the approved aircraft POH at hand as well as a Load sheet to be completed.

The aircraft is a Cessna C172.

Airfield                                   Bush Strip named ‘Somewhere in the Bush’

Surface Temp                        32° C

Field Elevation                      5,300 ft.

Field Length                          800 metres

To 50 foot obstacle              1050 metres.

Surface –                               grass.

QNH                                       1023

Trip fuel                                  required is 24 usg (the sortie involved offers no other on

route stops and in order to comply you are compelled to

carry enough fuel in order to have 45 minutes of reserve

fuel at your destination or destination alternate if required

Pilot                                        80kg

Front Passenger                   80kg

2 rear passengers                 80kg each

Baggage                                100lbs

Using the POH and an appropriate Load-Sheet let’s see if a take off from this airfield is possible under the set of circumstances.

mb_6

 

mb_7

mb_8

What is your verdict?

 Is the Aircraft overloaded? ……………………by how much?………………………….

Is the C of G in limits? ……………………

Is this acceptable? …………………………

How can we rectify the Mass and Balance Problem?

 We must reduce the weight of the load to be carried and at the same time ensure that the C of G is within the Envelope.

The hundred pounds of baggage is toward the back of the cabin so if we moved it forward and placed it on the floor between the pilot’s seat and the back seats it would probably solve the C of G problem but then you would have to send one of your passengers home by train because the weight limitation will still be exceeded.

It would be better to send the baggage home by train perhaps?.

We like our friends so let’s rather send the baggage home by train!

mb_9

“Great that fixes that! We are all G for Go!”

 Not so fast !  What about WAT?

mb_10

From the Take Off Data chart above:

Enter at MAUW 2,300 lbs

No Head Wind

5,000 ft Pressure Alt.

Read the Ground Run = 1255 ft

Read the 50 ft obstacle = 2480 ft

But note that this is at ISA standard temperature of 41°F at  Pressure Alt of 5,000 ft. (5°C)

The Temperature is 32°C Which means the actual conditions are ISA + 27°C (CONVERTED TO °F = 81°F above standard)

Now see what the notes in the Take Off Data table say “ for every 25°F above standard (41°F) increase the take off performance figures by 10%. (81°F ÷ 25°F= 3.24 = 32.4%)

Now apply this to the Take Off Ground Run (1225 ft + 32.4%) = 1,622 ft

Convert this to Meters = 494.38 Meters! Great the runway is 800 meters long! No problem!

“Uh Oh! The table says I must add on 7% for a dry grass runway, which it is. So, still O.K. that = a Take Off Ground run of 1,735 ft, Still only 528.82 meters.

Easy stuff! So I guess we can go now!”

“HOLD YOUR HORSES! there are trees 1050 meters from the threshold which are 50 meters tall!”

“But they are more than a kilometer away from where we start our Take Off Roll!

Don’t be ridiculous now!”

“Not ridiculous, HAVE A LOOK AT THE TABLE!”

The table shows that to clear a 50 ft obstacle we only need 2,489 ft (758.64 meters)

That is true for Standard Temperatures but read it again carefully, it clearly states to add on 10% for every 25°F above Standard and 7% for a dry grass runway.

So the same calculation applies:

2,489 ft + 32.4% = 3295 ft + 7% (grass runway) = 3526 ft (1074.72 Meters)

“We are not going to clear the trees at the end of the runway which are 1,050 meters from the take off threshold !”

Still no go!

Now what?

What if we reduced the baggage to 75 lbs and sent 1 passenger home by train with his baggage (25 Lbs) ?

The Take off condition will now be 2,195 lbs (rounded off to 2,200 lbs)

Let’s see how this works in terms of WAT.

Under Standard Conditions at 5,000 ft Pressure Altitude.

Take Off distance at  2,300 lbs      =       2,480 ft.

Take Off distance at  2,000 lbs      =       1,625 ft

Difference                    300 lbs       =          855 ft

So we can interpolate the Take Off Data Chart as follows:

855 ft ÷ 3 (00) lbs = 285 ft.

So for every 100 lbs above the 2,000 lb reference on the T/Off Data Chart we must add on 285 ft to the Take Off Distance (50 ft obstacle).

The sum then: 1,625 ft + (2 x 285 ft ) 570 ft = 2195 ft.

Now add 32.4% to this for deviation from ISA temperature and & 7% for the Grass Runway.

2,195 ft + 32.4% = 2906 ft + 7% = 3109 ft.

Convert to meters = 948 meters.

Finally, this we can do but at the price of sending one of our 80 kg passengers home with his own 25 lbs of baggage.  

The question is, how come are you’re here with this load?

At least you considered the Threats and Risks involved for this departure by considering all of the facts and understanding the POH and limitations of your aircraft performance under certain conditions.

Had this not been the case perhaps all would have ended up going home by train but in the goods department.

Now let’s see what your Load Sheet looks like for your flight out of ‘ Some Where in the Bush’ as well as arrival at home base with close to minimum legal fuel requirements.

Referring to all information available is all in order?

 mb_11

What other threats can you think of that could be applicable to a departure from a ‘hot and high’ airfield?

  • Rate of Climb to clear obstacles within the vicinity of the airfield of departure.
  • The fact that Rate of Climb will decrease substantially when turning to clear obstacles in the vicinity of the departure.
  • Not factored into the Rate of Climb Data are downdrafts and wind shear caused by thermals and topographical features in the vicinity.

Take a look at this MAXIMUM RATE OF CLIMB TABLE.

mb_12

From the Take Off Data mentioned before at the departure airfield we know that the conditions are ISA + 81° F (27°C) above Standard.

Look at the Table for 5,000 ft and at Gross 2,300 lbs, it states a climb performance of 435 ft per minute. Read further and it says to adjust this performance by 20 ft per minute (decrease) for every 10° F above Standard Temperature.

81° F ÷ 10° F = 8.1 x 20 = 162 ft per minute.

So a Climb Performance of only 273 ft per minute can be expected!    

Not much! Add to this the fact that should you need to turn to clear an obstacle in the vicinity of the departure airfield this rate will decrease substantially.

TAKE OFF DATA SHEET.

It is always good policy to complete a Take Off Data Sheet:

  • It will help you to recognize threats.
  • It will help to form a plan and make adjustments to preconceived ideas.
  • It will alert you to possible actions and options in the event of an emergency.
  • Most importantly, it will get you thinking!

mb_13

How does this Take Off Data Sheet compare to your departure details after all adjustments were made?

Remember that Density Altitude also affects the aircrafts landing performance and a longer landing roll must be factored in when operating at ‘Hot and High’ airfields.

The work that we did above required quite a bit of thought in terms of converting values and interpolation of figures obtained from graphs and tables.

Some aircraft manufacturers make the task easier for later models, see the Take Of Performance graph below:

mb_14

Simply enter 32°C on the graph and move vertically up to Pressure Altitude 5,000 ft. From this intersection move horizontally across to the Weight Reference Line. Then parallel the lines to Loaded Weight of the aircraft, say 2,400 lbs.  Then horizontal to the Wind Ref. Line, then parallel and down to 5 kt Tailwind. Straight across to Ground Roll 1,800 ft. and parallel and up to 50 foot Obstacle 3,090 ft.m