Last minute performance questions

[Just another student]

I have a quick question that has crept up in some feedback that I have seen.

Putting in 16500 litres of fuel with a sg of 780Kg/m3 and writing 16500kg of fuel on the load sheet will result in?

a) TOD increasing and ASD decreasing and v2 being too fast
b)TOD and ASD decreasing, V2 too fast
c)TOD and ASD remain constant etc
d)TOD and ASD increasing if calc speeds are used

Am I to assume that the sg figure is a type error, and that it means 0.78 sg? That would seem a far more likely figure to me, as most sg's I have used are in that region. This would mean you have put in 16500 x 0.78 12870 kgs of fuel, making TOD decrease, ASD decrease and V2 too fast.

Am I correct in saying this?

Cheers

I've just realised that 780/1000 (the sg of water) would be an equivalent of 78%. But is the method of my answer correct?

[Just another student]

In the climb an aircraft has a thrust to weight ratio of 1:4 and a lift to drag ratio of 12:1. While ignoring the slight difference between lift and weight in a climb, the climb gradient will be?

a 3.0%
b 8.3%
c 16.7%
d 3.3%

Could someone please work through this question for me, the answer given is c 16.7% . I am trying to work through it, but my mind has gone blank for the moment.

Cheers

[Keith.Williams.]

In your first question the aircraft is lighter than you think it is, so your calculated TOD, ASD and V2 will all be too high.

The wording of the options is a bit dodgy (which probably means that it is what actually appeared in a JAR exam paper), but option b is the most accurate. TOD and ASD will not really decrease, but they will be less than you expected them to be. Among other things V2 min is a function of Vsr, so your over-estimation of the weight will cause you to over-estimte V2.


In your second question you must remember that % climb gradient is approximately 100% x (Thrust - drag) / weight

This can be rewritten as

100% x (Thrust/weight - Drag/weight)... Let's call this rquation 2.

Thrust/weight is the thrust to weight ratio and the question gives this as 1 to 4, which is 1/4

The question also states that the lift to drag ratio (which is Lift/Drag) = 12/1.

If we ignore the slight change in load factor in a climb we can say taht lift = weight. This enables us to rewrite the last equation as

Weight/drag = 12/1

Turning both sides of this equation upside down gives

Drag/Weight = 1/12

So yhrust/weight = 1/4 and drag/weight = 1/12

Putting these values into equation 2 gives

% gradient = 100% x 1/4 - 1/12

This is 100% x 0.1666667 Which is about 16.7%








So we now have % gradient =

[Just another student]

Thanks Keith :ok:

[Dick Whittingham]

Or, to put it another way:

Thrust = 1
Weight = 4
Drag = 1/12th of 4, or 1/3

T - D = 2/3

Climb Angle = 2/3 divided by 4, = 1.67radians, or 16.7gradient

Dick W

For the mathematically minded this uses two approximations, that Cos of small angles is 1 and that the tangent of small angles is the same as the angle itself in radians.

[Tinstaafl]

1 cubic metre of H2O weighs 1000kg. By definition the SG=1 (it's water...)_

If you have a different substance that weighs 780kg/m^3 then it must be

780
-------- = .78 SG
1000


In other words, they gave you the fundamentals of SG & expect you to to know enough about SG to recognise it when presented in a different form.