Mass & Balance Questions - Help!

[JetMouse]

Hello could someone help me through the following questions - thanks!

Q1.
If a compartment takes a maximum load of 500kg, with a running load of 350kg/m and a distribution load of 300 kg/m2 max. Which of the following 500kg boxes can be carried?

1. 100cm x 110cm x 145cm
2. 125cm x 135cm x 142cm
3. 120cm x 140cm x 143cm
4. 125cm x 135cm x 144cm


Q2.
An aircraft takes off as normal on a scheduled flight however, shortly after take off it is diverted to another airfield.

MSTOM 14000kg
PLTOM 12690kg
MSLM 9600kg
Trip fuel to original dest. 6000kg
Contingency fuel 200kg
Alternate fuel 200kg
Final reserve fuel 750kg
Expected landing mass at orig. dest. 4600kg
fuel consumption 1,500kg per hour
Actual flight duration 2 hours
PLLM at diversion airfield 9000kg

Can the aircraft land safely at the diversion airfield?


Q3.
A twin engine aircraft is certified for a max. structural TOM of 58000kg and a max. LM of 55000kg. Given the information below what is the limiting take off mass of the aeroplane?

PLTOM 61000kg
PLLM 54000kg
MZFM 36000kg
OM 55000kg
Trip fuel 3000kg
contingency fuel 150kg
alternate fuel 500kg
final reserve fuel 500kg
flight duration 3 hours
fuel consumption 500kg per engine per hour


Many thanks for the help - workings out would be appreciated!
JM

[BigAir]

Ah Mass and Boulois, one of my favourites....

Q1. First see if you can use the running load limitation of 350 kg/m to remove some answers. To do this take the mass of the box (500kg) and divide it by the longest edge of each box. Doing this you will find that the 142cm box has a running load of 352kg/m, which is out of limits, so you can rule out number 2, all the others are in the running load limit.

Next you want to see what the distribution loading limits are like, to do this work out the biggest area that each box could be then divide the mass of the box by the areas to see which ones are in limits, so for the answers:

1) 1.1m x 1.45m = 1.595 m2, 500/1.595 = 313.48 kg/m2
2) out of running load limit
3) 1.4m x 1.43m = 2.002 m2, 500/2.002 = 249.75 kg/m2
4) 1.35m x 1.44m = 1.944m2, 500/1.944 = 257.2 kg/m2

So boxes 3 and 4 are both able to be carried!

Q2. First you need to work out the actual take off mass, you get this by taking the expected landing mass at original destination (4600kg) and adding the trip fuel to original destination (6000kg), so the actual TOM is 10600kg. You know the actual flight time is 2 hrs and fuel burn is 1500kg per hour so 10600-(2x1500) = 7600 kg for landing mass; PLLM is 9000kg, so you are okay to land - the rest of the info is there to confuse you!

Q3. This is easiest to do by using a pencil on the sample load sheet at the back of CAP 697/8 (whichever one it is), just write the figures in the relevant box and you take the most limiting one. A trap on this question is that STOM is less than PLTOM!!! I don't have my CAP manual anymore and my hangover is preventing me from working this through in my brain, but if you use the CAP manual it should make sense.

BigAir

[JetMouse]

Thanks for the help BigAir - much easier when you know how!

mmm one other question!

An aircraft is flying at 1.3 Vs1g in order to provide adequate margin above the low speed buffet and transonic speeds. If the mass increased from 285,000kg to 320,000kg and 1.3Vs1g is 180kts CAS at 285,000kg what is the new 1.3 Vs1g?

Thanks again...

[The Greaser]

i think new stall speed is proportional to square root of the increase in weight ie.

Square Root (320000/285000) = 1.0596

So new 1.3Vs = 180*1.0596 = 190.73 kts

For question 3 i would suggest max takeoff weight will be restricted by performance limited landing mass which is 54000, trip fuel is 3000 so max takeoff weight is 57000.

[OneIn60rule]

I also believe the answer to be 57000.

Just based on fact that the PLLM is lower than MLM, MaxTOM is lower than PLTOM.

So the only numbers that should be used in the Cap are PLLM, MAXTOM and MZF.


On the money here or right out?