How far will an aircraft travel in 2-1/2 minutes with a groundspeed of 98 knots?
 

How far will an aircraft travel in 2-1/2 minutes with a groundspeed of 98 knots?

I understand the answer is 4.08NM

But I want to know how one would calculate the answer?

(98/60)*2.5

2,5 minutes equals 0.04167 hours. 2.5/60

98 knots is 98 nautical miles per hour.

0.04167 hours times 98 nautical miles per hour equals 4.083 nm


(you should know this from kindergarten) :=

I'm hoping he meant an easy way to calculate it in his head... There are 60 minutes in an hour. So 98kts is just a little over 1.6kts per minute x 2 then add .5 which equals 4. Close enough for doing the calculations in your head.

This is a late April Fools question?

You'll find I am more than happy to answer serious ATPL level questions on this forum but this is beyond a joke. Others have answered your question.

The profile for Spencer indicates that he is currently working towards his PPL so we should not be too surprised that he is asking this type of question.

1 knot is 1 nautical mile per hour.

This means that 98 knots is 98 nautical miles per hour.

There are 60 minutes in an hour so if we divide 98 by 60 we will convert 98 nautical miles per hour into 1.633 nautical miles per minute.

If we then multiply this by 2.5 minutes we will get the number of nautical miles flown in 2.5 minutes. 2.5 X 1.633 is 4.0825

Assuming there is no wind?:cool:

I just thought 2½ min at 1½ mi/min plus 10% would be near enough...

So, in my head, that's 3+¾, i.e. 3.75, plus .37 is a tadge over 4 nm.

I appreciate the help. As Keith said I've just begun my PPL.

It should be fairly obvious from the replies above, for a no wind day - but wind will completely change the situation - hence the infamous 'whizz wheel' where you can graphically add the wind vector and then derive groundspeed.

Or you could ball park it with the wind direction degrees of beam, i use the "6" method ie. if the wind is 30 degrees of beam its 3/6 (half) the wind speed decducted from the GS, if its anything more than 60 degrees (6, 6's) deduct the full wind speed.

If I have this wrong I will gladly be corrected.

Two answers.

On the ground, real calculation -> 98 knots equal 98 nautical miles per 1 hour equal 60 minutes, so the 2.5/60 fraction of 98 nautical miles = (2.5/60)*98 = 4.083 nauticals

In the air, head calculation -> 98 knots is almost 90 knots +10% and 90 knots is 1.5 nauticals per minute, 1.5 times 2.5 is 3.75 plus 10% roughly equals 4.1 nauticals - good enough

The most memorable math class I ever had in school saw a surprise test. It was simple math, but big, awkward numbers, and lots of them. The teacher told us that we would not have time to calculate them all (and calculators - to be honest, had not been invented yet). He told us that nearly all the math we would ever do in life would be used to make a decision. The result would direct us to a "yes" or a "no". So, if we were pressed for time, a close guess would probably result in the correct decision. The purpose of the test was for us to guess at the answer. If our guess was within 10% of the correct answer, we would get the mark.

This logic is very prevalent in piloting. You'll need to make many decisions, most usually, do I have enough fuel to get there? The good guess, with a bit of conservatism, will be adequate.

I do not imagine a situation where based on the groundspeed of a GA aircraft, there is a need to know the distance covered to within 1/100 of a mile. For my experience the nearest mile, or 5% for greater distances has met the need every time. That said, during training and exams, the questions might force greater precision, as you choose the best of two possible multiple choice answers. Know the theory, but know when to apply it too!

This depends on whether you need an absolute to the thou or a ball park guesstimate for navigation.
98 (nearly 100kts) which is 1.6 per min, times 2.5 = about 4.

Some the answers / remarks given here fall in to the category of RTFQ, were does the wind come in to the calculation ?

I'm not saying the OP should ball park it for his PPL studies but once in the real world just divide it up into multiples of 6.

90 kts=1.5 nm minute

96kts=1.6 nm minute

102kts= 1.7nm minute etc.

98 kts is nearest to 96 so just multiply 1.6 by 2.5 which equals 4.0. If you're feeling particularly anal bung a bit on for the wife and kids.

Piperboy: you don't have it wrong, I use the same method. It's just the sine of the wind angle. 60 degrees off would actually be 0.866 but it's near enough to one for me. I use the same method for xwind component on takeoff/landing, which is what your drift angle is anyway.

Come on, wouldn't be Prune without people jumping in at the deep end!

I'm missing some crucial information: is the aircraft going in circles or in a straight line? :ugh:

Guys, keep it stupid simple ... lets take the easy road with ground meaning no wind, perpendicular to gravitational forces -> if it would be groundspeed along gravitational force the typical GA plane won't make 2.5 minutes ... :ugh::ugh::ugh:

Many moons ago (before computer accounting software was available to small companies) I hired a lady who's primary job was to gather all the sales tax information for the different jobs and equipment sales we had done that month and compute the sales tax (VAT in UK) we had to remit to the government. At that time the company turnover was usually about $100,000 per month,the sales tax rate was 8.25% and almost all our sales were sales tax eligible. After her first month she walked in and presented me with a check for approximtley $84,000 to sign for mailing to the tax office. I asked her if we had had an unusally large sale that month (knowing we hadn't) to which she said no, revenue was just over $100,000. I suggested she check her math and she threw a wobbler about me questioning her professionalism and how rude it was of me to doubt her numbers based on her many years of being a accounting dept sales tax expert.

Bottom line, I thought to myself, is she cant start out with a ballpark number in her head and then work the actual figures that will verify her "guesstimate" then she is going to bankrupt me sooner or later and out the door she went.

Always start out with a rough mental calculation before working out the exact number.

The discussion about precision is interesting. Though by no means an expert in math, I have some familiarity with precision and rounding numbers. The OP presented the time as "2 1/2 minutes". This would presumably equate to 2.5 minutes. Therefore the actual time value could be 2.25 to 2.74 minutes, if I have it right. Thus, working out the distance to 0.01 miles would be not entirely appropriate, if the time is being expressed to only 0.1.

But, that's semantics, for entertainment. Consider why you need the answer, and that may point the required precision. In this case, to pass a groundschool exam, you may as well get the number right on - just know that in many cases in the real world, that's not needed...

To get an exact answer for a test, posters have already showed the correct formula.

For in flight use what you really want is TLAR (That Looks About Right) skills.

This means using easy approximations to get a "good enough" number.

So in for your original question "how far will I go at 98 kts in 2 1/2 mins" I would do the quick mental calculation as follows.

-Round up or down to the nearest 1/2 mile per min ( ie 60 kts = 1 mile/min, 90 kts = 1 1/2 mile/min 120 kts = 2 mile/min. Therefore 98 kts is closer to 90 than 120 so use 1 1/2 mile/min value

- calculate the whole numbers first than add the remainder. so 2 times 1.5 = 3 miles plus half of 1.5 ( for the remaining 1/2 min )= 3/4 gives you 3 + 3/4 = 4 1/4 miles an answer that is close enough.

You can do this in your head in maybe 2 seconds. For in flight calculations it will be rare that a calculation of this kind will not be good enough. If you need more accuracy you should use a Whiz Wheel but again a mental TLAR calculation is a good check.

Precision: Shirley 98 divided by 60 = 1.633333333333 per minute, times 2.5 minutes = 4.08333333333. Or have I missed something?
The difference between that and my original "about 4" is, you will travel a further 506.666464 yards, provided there are 6080yards in a nautical mile?
If the answer governs the decision to go for a landing at home base or not because in 2.5minutes it will be 30mins after sunset and you will be illegal, so a landing at a closer airfield may be required, then absolute precision may be necessary. If this is to pass an exam question then pick the closest of the multiple choices, if it is a general practical Nav question then by the time you have figured it out you will be there already. If you read all my crap first you will be well past it and the whole thing will be irreverent.

Hey Crash One, I think you meant 'feet' not 'yards'. ;)

Which is a nice segue into an issue which has bedeviled my business, oil exploration. Depending where I am in the world, the units can be SI, or Imperial or a mixture! Then on top of that, historical documents can be in different units.

Some time ago, a colleague was having a problem with data from a document showing the depths to geological formations ("tops") in a exploration well and asked me to take a look. The numbers did not pass the BPF's TLAR test.

"Are these tops about three times bigger than you were expecting?"
"Yes. Why?"
"You've got a feet to metres problem."

For me, 2.5 minutes is 1/24th of an hour (5 minutes is 1/12th), which is very close to 1/25th, just as 98 Kts is damn close to 100.

So 1/25th of 100 is 4 NM, near as dammit the answer.

FBW

My mistake, no wonder my navigation is bluddy rubbish :ugh:

I'm still trying to work out the real world case for wanting to do such a sum.

I can see it the other way around - "at 98 knots how long will it take to go four miles" is part of answering the "report your estimate for the beacon" question.

As usual we are looking at the question from the wrong end of the telescope.

Simply slow down to a G/S of 60kts - enjoy the view - and have no further problems with mental maths :)

Wasn't there a space probe to Mars that went spectacularly tits up because someone used imperial measurements instead of metric?

Forget the PPL, this is a high school type question. :rolleyes:

No you're not. The aircraft will travel 4.08 nms whether it's flown in circles or not. The question did not ask how much closer to a particular point the aircraft would be after 2.5 mins at a G/S of 98 kts. Since the question mentioned groundspeed specifically then it matters not in which direction(s) the aircraft was flown.

Nobody has yet asked,-"are you carrying a coconut"
exit to strains of "the white cliffs of dover"


some folks here......no sense of humour :*

Yes, the Mars Climate Orbiter which entered the Martian atmosphere on the wrong trajectory and burnt up, due to a major units error.

Steve, we are armed coconutians and You don't frighten us, English pig-dogs! Go and boil your bottoms, sons of a silly person. I blow my nose at you, so-called Arthur-king, you and all your silly English kaniggets. Thppppt! [THE GUARD] Wasn't there a discussion on a swallow and a one pounds coconut with regards to the groundspeed question, but if I remember correctly they argued on airspeed for the swallow, not groundspeed? Now remains the question how to get the 43 times per seconds wings beat on a Cessna? Ok, ok, ok, weather is brilliant and I'm better off in the cockpit.

Wasn't there some other piece of expensive hardware that got its feet tangled up with metres and looking for a mountain to align with wandered off trying to find a planet with a 25000 metre high mountain?

7.56km (for some reason glider pilots calculate distance in km, height in ft, speed in knts and weight in pounds or kg! Confusing)

Visibility in metres, Nav distances in nautical miles, heights in feet, Nav tracks in deg true, wind in deg magnetic, fuel in litres, imp gallons, US gallons, pounds, or kilograms, weights in pounds or kilograms, No wonder we get confused, wasn't there a guy called British Standards?

Working as a chemist in industry one learned very quickly to change from g/litre, oz./gall (Imperial), oz./gall US, degrees Centigrade and Fahrenheit.

I also received some good lessons in the use of precise terms such as the difference between 2 1/2 and 2.5. I once went to the Toolroom foreman, a God in the motor industry in the 60's, and asked for a strip of steel 0.5 in. wide.

He asked if I really wanted it 0.5 in. wide and I said yes, half an inch. "But you've written 0.5 in.", he said rather scornfully. "Yes, I said, Half an inch" .

Eventually, he patiently explained to me the error of my ways, a lesson I have never forgotten.

I also learned the difference between precision and accuracy and was amazed how many professional technicians didn't. This became embarrassingly obvious when the calculator and digital instrumentation became readily available.

This isn't directed at the OP who is studying for his PPL and must do it correctly but I'm always a little bemused when people argue the toss between 100 kts and a 101 kts when discussing GA flying. A very short while after my license issue and a few hours flying in the real world I quickly came to the conclusion that everything in GA is plus or minus 5.

I took some friends flying to North Yorkshire the other day, neither of them experienced in GA flying. The usual questions of 'How high and how fast will we go' were met with '130kts and 3,000 feet.' It was very thermic over the moors and as the ASI went between 125-135 kts and the altitude did it's best to shove me around while I was trying to keep within a couple of degrees of my planned course and failing I was thinking 'It's all plus or minus 10 actually'.