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Basic aviation Mathematics


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Hi everyone,

I was just wondering if I could pick your brains about a few things!

On friday I have an interview to get into a university course for an Aviation Science Diploma. I have most bases covered but they said there is a basic maths test involved. I can do basic maths in my head without a worry e.g. addition, subtraction, multiplication, division, fractions, percentages etc but the word maths always makes me stress a little .

I was wondering if anyone knew what sort of questions I might encounter? They said mostly just speed/time problems. So just wondering if you guys had any helpful tips, tricks or hints for me. Anything would be much appreciated! Just trying to get an edge here so I can ace this thing.

I am looking forward to this!

Eagerly awaiting your replies.

Thanks for all your help

Tom

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Rate X Time = Distance

ie..At 480 kts, how long will it take you to go 15 miles?

(480 kts is 8 miles per minute..so about 1 minute 49 seconds)

You can solve for any of the three variables. Doesn't have to be time/speed/distance either. You could use the same formula to figure a problem like:

You can dump fuel at 2400 pounds per hour. How long will it take to dump 18000 pounds?

Stuff like that-

HTH

Pig

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I sure hope you're just throwing out silly examples because I'd hate to be anywhere near plane needing to dump 18k pounds of fuel!

Uh.....

Hate to break your bubble, but Pig's example is for a likely scenario.

Agree you'd want to be nowhere near the aircraft when it's dumping fuel. That's why it's typically done at higher altitudes (allowing the fuel to vapourize into the air) and over unpopulated regions if at all possible.

In the case where an airliner takes off with a few hundred thousand pounds of fuel, and a maximum landing weight that is far below its weight with fuel on board, imagine a scenario where a problem is encountered that makes an immediate landing advisable. One scenario is a passenger has a heart attack during take-off, and the pilots want to land ASAP to get him to hospital.

ALF

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My point was dumping that much fuel meant a non-routine situation and I wouldn't want to be nearby.

Totally understandable - me neither!

Generally when fuel dumping is in progress, air traffic control makes transmissions on emergency frequencies to warn other aircraft to steer clear.

ALF

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Percent of M.A.C. as defined by a loadmaster student at Sheppard A.F.B.

Percent of MAC: Two all beef patties, special sauce, lettuce, cheese, pickles, onions on a sesemee seed bun.

He wasn't asked another question for a couple weeks.

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When I was a kid - I was always told that I'd need a lot of math and science courses to be a pilot. I've been doing it for 33 years now, and I've never had to do anything more than add, subtract, multiply or divide. Your flight plan may vary.

Hitch

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Uh.....

Hate to break your bubble, but Pig's example is for a likely scenario.

Agree you'd want to be nowhere near the aircraft when it's dumping fuel. That's why it's typically done at higher altitudes (allowing the fuel to vapourize into the air) and over unpopulated regions if at all possible.

In the case where an airliner takes off with a few hundred thousand pounds of fuel, and a maximum landing weight that is far below its weight with fuel on board, imagine a scenario where a problem is encountered that makes an immediate landing advisable. One scenario is a passenger has a heart attack during take-off, and the pilots want to land ASAP to get him to hospital.

ALF

Considering in the example given the dumping of fuel would take 7.5 hours it might be quicker just to continue to the destination :thumbsup: (I'm assuming a typo).

As for the questions, sounds like they'll be of the following type (disclaimer: I'm just going off the information in the OP, don't have any idea what an Aviation Science diploma entails, much less the basic maths test)

The distance between point A and point B is 350 nautical miles, the aircraft has a ground speed of 100 knots. How long does it take to cover the distance?

time = distance/speed = 350/100 = 3.5 hours

The distance between point A and point B is 150 nautical miles, the aircraft has covered this distance in 2 hours, what is its airspeed?

speed = distance/time = 150/2 = 75kts

The aircraft flies for 2 hours at a speed of 125 kts, what distance has it covered?

distance = speed * time = 2*125 = 250 nm

Bonus question for practising trigonometry (though by the sound of it you wont be needing it)

The aircraft is flying on course 000 with an airspeed of 150 kts. The wind is 20 kts at 060, what is the aircraft's groundspeed?

Headwind component is cos(60)*20 = 0.5*20 =10 kts

So ground speed = 150-10 = 140 kts

Answers should be correct, but feel free to point out any mistakes I may have made.

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Considering in the example given the dumping of fuel would take 7.5 hours it might be quicker just to continue to the destination :whistle: (I'm assuming a typo).

Sorry, but I'm puzzled at how you could make a calculation based on my general comment. I didn't give any of the required information:

-How much fuel on board exactly?

-Fuel burn anticipated while completing approach to selected airport (which may be a different one, with a longer runway or better medical facilities)?

-Zero-fuel weight of aircraft?

-Weight of cargo, pax, etc?

-Maximum landing weight?

-Fuel dumping rate?

Each aircraft has its own numbers. In my example of an airliner, it would have to be one of the biggest and heaviest (think A-340, B-747, A-380). Logically, it would have a very high fuel dumping rate, in keeping with the huge amounts of fuel it can carry. I don't know much about the type certification rules, but it would seem to me that it would be a requirement to have a high dump rate for a big, heavy aircraft. Finally, these aircraft can land with lots of fuel on board. I never said that all 300,000 lbs would have to be dumped...

Not trying to start a flame war, but simply pointing out that I did in fact think through my comment before posting.

ALF

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ALF, I believe Johnny_7713 was referring to Pig's example cited above of dumping 18,000LBS at a rate of 2400 LBS per hour. I suspect Pig meant a dump rate closer to something in "pounds per minute" with regards to fuel dump capability.

Cheers, Mitch

Doh!

Thanks for pointing that out Mitch.

Jonny_7713 - sorry dude! Guess I'm just feeling unusually defensive today...

ALF

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The suggested items are fine, but they won't do you a whole lot of good if you take off with the CG outside of the limits. You might consider reviewing how to calculate the CG from the moments and weights.

Certainly a useful skill, but tomthegrom said the maths test would focus mainly on speed / time problems. Calculating the CG position sounds like something you would learn at the course, rather than something you would already be expected to know for the entrance exam. Of course, as I said before, I'm just guessing what will be in the exam based on the comments quoted in the OP.

Alf18 - No problem, should have made it clearer I was referring to Pig's example

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ALF, I believe Johnny_7713 was referring to Pig's example cited above of dumping 18,000LBS at a rate of 2400 LBS per hour. I suspect Pig meant a dump rate closer to something in "pounds per minute" with regards to fuel dump capability.

Cheers, Mitch

Yep. There you go. Typed too fast...Pounds per minute-

Regards,

Pig

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I sure hope you're just throwing out silly examples because I'd hate to be anywhere near plane needing to dump 18k pounds of fuel!

Do you know what a fully loaded 747-400 would have to dump to get down to minimum landing weight if something bad happened just after takeoff? I guarantee it's a LOT more than 18,000 lbs that's gotta go!

BTW, if I may only offer one tiny piece of advice for you at the outset of your aviation career, let it be this:

Waaaaaay back in the back of your head, just under that little notch above your neck, lives a little voice. This is the little voice that says things like "That's really stupid, don't do it!" (just before you hand your beer to your buddy so you can light the fuse). It's what makes the hair on the back of your neck stand up just before you step on the rusty nail. Are you familiar with that little voice? If not, get familiar with it. It knows stuff. And my advice is, always, always, always, always listen to that little voice. If it says "Something's just not right here", then something's not right. If it says "I wouldn't do that!" then don't do that. You'll stay alive a lot longer. Oh, and I never say "always" or "never" :D

J

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Do you know what a fully loaded 747-400 would have to dump to get down to minimum landing weight if something bad happened just after takeoff? I guarantee it's a LOT more than 18,000 lbs that's gotta go!
And, as I replied to Alf, I don't want to be anywhere near were that necessary! Edited by Slartibartfast
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