Mental maths - tips, tricks and shortcuts
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Does anyone notice how when they first learned to drive a car, they had to really work on clutch & gear coordination, parking, hill starts etc...?
Use a calculalor if you must. Use a wizz wheel if you must. Use your brain if you must.
Whatever you do. Do not get caught up in 15th century training methods.
Last edited by Zoomy; 31st Dec 2012 at 02:06.
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You know, remember the abacus.
All of the training I received in GA, was pedagogical. It was mainly teacher centered with the learner being a passive receiver. Information flowed one way and all the learning activities in the class room were rigid sequences.
Adults, (usually socially accepted as 18+ give or take a few years in some), learn in a completely different way. In fact it has been proven that some children learn in an andragogical learning environment.
Adults learn best when new information is linked to past experience, we all know that. But adults also like to take part in the learning path and have some form of input into the sequence.
If a student presents with a calculator, so be it. This is a result of the present. They are widely used in schools and kids grow up with them. If you want to ween them off, do so nicely. There is absolutely no need to throw the thing in the hat shelf and tell the student off. Perhaps show them the mental arithmetic techniques as the present themselves.
Some of the rhetoric on here regarding a students inability to calculate simple sums, just tells me the instructor has no patience for the job at hand.
All of the training I received in GA, was pedagogical. It was mainly teacher centered with the learner being a passive receiver. Information flowed one way and all the learning activities in the class room were rigid sequences.
Adults, (usually socially accepted as 18+ give or take a few years in some), learn in a completely different way. In fact it has been proven that some children learn in an andragogical learning environment.
Adults learn best when new information is linked to past experience, we all know that. But adults also like to take part in the learning path and have some form of input into the sequence.
If a student presents with a calculator, so be it. This is a result of the present. They are widely used in schools and kids grow up with them. If you want to ween them off, do so nicely. There is absolutely no need to throw the thing in the hat shelf and tell the student off. Perhaps show them the mental arithmetic techniques as the present themselves.
Some of the rhetoric on here regarding a students inability to calculate simple sums, just tells me the instructor has no patience for the job at hand.
Last edited by Zoomy; 1st Jan 2013 at 06:18.
OK, Zoomy,
What an unmitigated heap of steaming crap. How does your argument hold up when driving a base model Hyundai (ie. no power steering, AWD, ABS, rear camera etc etc etc). Spose your spelling is another example of near enough good enough, eh?
It got easier because you practised and used the skills. Same thing happens with mental arithmatic.
According to your logic, what's next? A licence based on age of the aircraft? Or an "easy to fly" licence vs a "hard" category?
I spend a significant amount of time explaining how to use a whiz wheel. I don't even charge when showing them some of the more advanced uses, such as multiplication and division. I show them alternatives to calculators as a means of cross checking flight planning. Divide the number by 10 and add half of that again to give 15%, a quick way to check variable fuel reserve as well as using a calculator for flight planning.
I explain to the student, regardless of their age, 18 or 48, why it is not a good idea to be using a device that sucks your attention into a tiny screen and funnily enough, not many older students have a problem with mental maths. People's skills have just gone rusty over the last 20 years, they haven't gotten dumber. (Maybe lazier, though.)
If the student continues to sneak calculators (even as far as onto their flight test, with the ATO quoting their head being inside the cockpit for so long as the biggest single reason they couldn't hold a heading or altitude, despite having flown the previous five navs without it no drama), I will continue to force them to use other methods and I do so with the full support of EVERY CFI I have flown under.
You know of a CFI who is happy to use calculators without any further effort, post their school up here, but only if you want to ensure their graduates don't find work, because I for one would be very cautious if I saw that particular school on a resume.
Continued reliance on a calculator will not, contrary to your babying, help a student, especially in the middle of a NVFR or IFR exercise with no autopilot. I have yet to see an ATO who prefers to see a calculator in a cockpit. Furthermore, if you are content with the ability and dedication of a pilot flying your family around commercially (or privately) who needs to take off their shoes and socks to add, then standards have hit rock bottom and started digging. I, however, refuse to promote this level of mediocrity.
Some of the "rhetoric here" is a result of
a) incredulous belief that students will refuse to make the effort to improve to the standard required of a professional pilot; and
b) "instructors" that are happy to accept this problem because it is "a result of the present".
I expect that level of complacency from hour building instructors, not anyone who is genuinely interested in producing the highest possible standard of pilot.
Not saying every student is a mental genius, but I will make the effort to help them if they want to help themselves.
I also noticed that as my cars progressed they got easier and easier to drive. Not because of my practice, but because of power steering, AWD, ABS, rear camera, ect ect ect.
It got easier because you practised and used the skills. Same thing happens with mental arithmatic.According to your logic, what's next? A licence based on age of the aircraft? Or an "easy to fly" licence vs a "hard" category?
I spend a significant amount of time explaining how to use a whiz wheel. I don't even charge when showing them some of the more advanced uses, such as multiplication and division. I show them alternatives to calculators as a means of cross checking flight planning. Divide the number by 10 and add half of that again to give 15%, a quick way to check variable fuel reserve as well as using a calculator for flight planning.
I explain to the student, regardless of their age, 18 or 48, why it is not a good idea to be using a device that sucks your attention into a tiny screen and funnily enough, not many older students have a problem with mental maths. People's skills have just gone rusty over the last 20 years, they haven't gotten dumber. (Maybe lazier, though.)
If the student continues to sneak calculators (even as far as onto their flight test, with the ATO quoting their head being inside the cockpit for so long as the biggest single reason they couldn't hold a heading or altitude, despite having flown the previous five navs without it no drama), I will continue to force them to use other methods and I do so with the full support of EVERY CFI I have flown under.
You know of a CFI who is happy to use calculators without any further effort, post their school up here, but only if you want to ensure their graduates don't find work, because I for one would be very cautious if I saw that particular school on a resume.
Continued reliance on a calculator will not, contrary to your babying, help a student, especially in the middle of a NVFR or IFR exercise with no autopilot. I have yet to see an ATO who prefers to see a calculator in a cockpit. Furthermore, if you are content with the ability and dedication of a pilot flying your family around commercially (or privately) who needs to take off their shoes and socks to add, then standards have hit rock bottom and started digging. I, however, refuse to promote this level of mediocrity.
Some of the "rhetoric here" is a result of
a) incredulous belief that students will refuse to make the effort to improve to the standard required of a professional pilot; and
b) "instructors" that are happy to accept this problem because it is "a result of the present".
I expect that level of complacency from hour building instructors, not anyone who is genuinely interested in producing the highest possible standard of pilot.
Not saying every student is a mental genius, but I will make the effort to help them if they want to help themselves.
Last edited by MakeItHappenCaptain; 1st Jan 2013 at 12:31.
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What an unmitigated heap of steaming crap.
Get A LIFE Mate.
Oh and as for the spelling, I forgot to use spell check.
standard required of a professional pilot
Last edited by Zoomy; 1st Jan 2013 at 21:13.
Why it is not a good idea to be using a device that sucks your attention into a tiny screen
This forum outlines the race to the bottom out industry faces.... If we can't get along in here we are doomed sitting 30cm away from each other in the pointy end, and even worse come EBA time.
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How is using a calculator any different to looking down at a map? Hell you can even hold the calculator up in front of your face if you have to.
I always round things up to make things easier to calculate. For fuel. 100lbs of Jet is around 54L. I round it up to 60L and work that out. Once you start taking bigger orders of fuel such as, for example, 1000lbs. For every 100lbs of fuel, you get 6 extra L. 6 x 10 = 60, 600 - 60 = 540L for 1000lbs. (I use this as an example, obviously if its 54L per 100lbs, for 1000lbs you just need to add an extra 0.)
ROD for glide slope is half your ground speed then add a 0 at the end.
My other options are a) Engage Captain Auto if I am single pilot and use a calculator. Or b) Get my F/o to either fly, or do the calculations.
I always round things up to make things easier to calculate. For fuel. 100lbs of Jet is around 54L. I round it up to 60L and work that out. Once you start taking bigger orders of fuel such as, for example, 1000lbs. For every 100lbs of fuel, you get 6 extra L. 6 x 10 = 60, 600 - 60 = 540L for 1000lbs. (I use this as an example, obviously if its 54L per 100lbs, for 1000lbs you just need to add an extra 0.)
ROD for glide slope is half your ground speed then add a 0 at the end.
My other options are a) Engage Captain Auto if I am single pilot and use a calculator. Or b) Get my F/o to either fly, or do the calculations.
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I just love the way that we Australians, in this industry are anal about the really important stuff like whether someone who uses a wizz wheel has higher moral ground than someone who uses a calculator, and whether someone who uses neither can claim themselves victorious.
Well I sneer upon you loathsome, dare I say unsafe masses, as I claim moral superiority; you see I have a wiz wheel on my over-sized Pilot watch which trumps you all.
As if my overt strutting wasn't enough, one glance at my watch by all and sundry, tells the great unwashed that I am a Pilot without having to actually say a word. This coupled with Ray-bans at a bar lets all those in "visual contact" make no mistake. I use words like "aircraft" instead of "plane" and extol the virtues of hand flying and make anti- automation comments whenever possible to mask my fear of it and the fact that I'm not really sure of what it all does.
Sometimes on a long flight I like to turn everything off and hand-fly my jet based on nothing more than memorised maps, pure skill and my trusty watch wizz wheel; usually after announcing "watch this". The fact that I can do this whilst complaining about Y gen (of which I am not) and randomly ranting about the government, single mothers, Airline management etc asserts my authority and prowess in the cockpit.
As for mental math tricks:
Multiplying by 5, 25, or 125
Multiplying by 5 is just multiplying by 10 and then dividing by 2. Note: To multiply by 10 just add a 0 to the end of the number.
12x5 = (12x10)/2 = 120/2 = 60.
Another example: 64x5 = 640/2 = 320.
And, 4286x5 = 42860/2 = 21430.
To multiply by 25 you multiply by 100 (just add two 0's to the end of the number) then divide by 4, since 100 = 25x4. Note: to divide by 4 you can just divide by 2 twice, since 2x2 = 4.
64x25 = 6400/4 = 3200/2 = 1600.
58x25 = 5800/4 = 2900/2 = 1450.
To multiply by 125, you multiply by 1000 then divide by 8 since 8x125 = 1000. Notice that 8 = 2x2x2. So, to divide by 1000 add three 0's to the number and divide by 2 three times.
32x125 = 32000/8 = 16000/4 = 8000/2 = 4000.
48x125 = 48000/8 = 24000/4 = 12000/2 = 6000.
Well I sneer upon you loathsome, dare I say unsafe masses, as I claim moral superiority; you see I have a wiz wheel on my over-sized Pilot watch which trumps you all.
As if my overt strutting wasn't enough, one glance at my watch by all and sundry, tells the great unwashed that I am a Pilot without having to actually say a word. This coupled with Ray-bans at a bar lets all those in "visual contact" make no mistake. I use words like "aircraft" instead of "plane" and extol the virtues of hand flying and make anti- automation comments whenever possible to mask my fear of it and the fact that I'm not really sure of what it all does.
Sometimes on a long flight I like to turn everything off and hand-fly my jet based on nothing more than memorised maps, pure skill and my trusty watch wizz wheel; usually after announcing "watch this". The fact that I can do this whilst complaining about Y gen (of which I am not) and randomly ranting about the government, single mothers, Airline management etc asserts my authority and prowess in the cockpit.
As for mental math tricks:
Multiplying by 5, 25, or 125
Multiplying by 5 is just multiplying by 10 and then dividing by 2. Note: To multiply by 10 just add a 0 to the end of the number.
12x5 = (12x10)/2 = 120/2 = 60.
Another example: 64x5 = 640/2 = 320.
And, 4286x5 = 42860/2 = 21430.
To multiply by 25 you multiply by 100 (just add two 0's to the end of the number) then divide by 4, since 100 = 25x4. Note: to divide by 4 you can just divide by 2 twice, since 2x2 = 4.
64x25 = 6400/4 = 3200/2 = 1600.
58x25 = 5800/4 = 2900/2 = 1450.
To multiply by 125, you multiply by 1000 then divide by 8 since 8x125 = 1000. Notice that 8 = 2x2x2. So, to divide by 1000 add three 0's to the number and divide by 2 three times.
32x125 = 32000/8 = 16000/4 = 8000/2 = 4000.
48x125 = 48000/8 = 24000/4 = 12000/2 = 6000.
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^^^^ 
On an every day operational basis, the only quick mental math I have to do is the Glideslope ROD. And thats about it.
Oh and ToD depending on which plane I use. Unpressurised. 500ft per minute is not a hard one.
Altitude x3 or x2 for pressurised aircraft.
GPS are now installed in pretty much every aircraft. And if not, DME is also there.
On an every day operational basis, the only quick mental math I have to do is the Glideslope ROD. And thats about it.
Oh and ToD depending on which plane I use. Unpressurised. 500ft per minute is not a hard one.
Altitude x3 or x2 for pressurised aircraft.
GPS are now installed in pretty much every aircraft. And if not, DME is also there.
To all, I will publicly apologise for letting my "enthusiasm" for the topic get away from me lately.
I have always admitted when I was wrong, but while I have been presenting my view with (too much) gusto, I still firmly believe in what I am saying and the principles behind it.
I was taught this way, have seen many different techniques, and don't believe that the aircraft most people are progressing into for their first "standard" GA job have changed over the last 20 years much. Still C210s with a few more GA8s maybe, so IMO, the techniques still apply.
Zoomy,
That is an out and out lie.
I have been known to send PM's to people apologising for undeserved public comments, but I do not use PMs to threaten. You may disagree with what I say, and it is my right to do so with your argument, but I do not behave as you are accusing and am more than happy for a moderator to look into the accusation, as I would do if someone threatened me.
I have always admitted when I was wrong, but while I have been presenting my view with (too much) gusto, I still firmly believe in what I am saying and the principles behind it.
I was taught this way, have seen many different techniques, and don't believe that the aircraft most people are progressing into for their first "standard" GA job have changed over the last 20 years much. Still C210s with a few more GA8s maybe, so IMO, the techniques still apply.
Zoomy,
sending other pruners threatening and intimidating PMs
I have been known to send PM's to people apologising for undeserved public comments, but I do not use PMs to threaten. You may disagree with what I say, and it is my right to do so with your argument, but I do not behave as you are accusing and am more than happy for a moderator to look into the accusation, as I would do if someone threatened me.
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Safe to say that MIHC is certainly passionate about what he teaches! A rare trait among most instructors these days.
In my earlier training days, my instructor thought that flying wasn't hard enough so he used to get me to count my 7,8, or 9 times tables backwards. Sounds easy, but try it during steep turns, if you don't get to 0, start again!
Call me a nerd but I loved those flights (and the challenge)
The reason why cars and flying machines are fitted with all these fancy bells and whistles is for one main objective, SAFETY.
I've made errors calculating my TOD before using my brain, how many times has my pocket calculator made them? 0. But a solid understanding and a mental check of the math confirms that.
Math is a requirement for all facets of flying.
Use all tools that are available in the cockpit, car or Segway to get you and your passengers safely to the destination.
I personally enjoy the challenge of using my noggin for calculations. But I'm not going to judge someone who doesn't enjoy maths as much as I!
In my earlier training days, my instructor thought that flying wasn't hard enough so he used to get me to count my 7,8, or 9 times tables backwards. Sounds easy, but try it during steep turns, if you don't get to 0, start again!
Call me a nerd but I loved those flights (and the challenge)
The reason why cars and flying machines are fitted with all these fancy bells and whistles is for one main objective, SAFETY.
I've made errors calculating my TOD before using my brain, how many times has my pocket calculator made them? 0. But a solid understanding and a mental check of the math confirms that.
Math is a requirement for all facets of flying.
Use all tools that are available in the cockpit, car or Segway
to get you and your passengers safely to the destination. I personally enjoy the challenge of using my noggin for calculations. But I'm not going to judge someone who doesn't enjoy maths as much as I!
A good thing to know is that:
100 fpm = 1 knot (roughly). (It comes from the fact that there's about 6000 ft in a nautical mile...)
This can help with calculating required climb RATES to meet missed approach obstacle clearance, as one example.
ie:
Vyse = 120 kts.
You need to make 2.5% gradient.
What RATE of climb (what the performance charts often speak about, and what the instrument tells you) do you / will you require?
2.5% of 120 is 3 kts.
So that's about 300 fpm...
Also,
2 knots = 1 metre per second
ie. halve the number on your ASI (convert to TAS first if significant) to know your speed in mps.
This stuff really should be taught. Maybe it is.
CR.
100 fpm = 1 knot (roughly). (It comes from the fact that there's about 6000 ft in a nautical mile...)
This can help with calculating required climb RATES to meet missed approach obstacle clearance, as one example.
ie:
Vyse = 120 kts.
You need to make 2.5% gradient.
What RATE of climb (what the performance charts often speak about, and what the instrument tells you) do you / will you require?
2.5% of 120 is 3 kts.
So that's about 300 fpm...
Also,
2 knots = 1 metre per second
ie. halve the number on your ASI (convert to TAS first if significant) to know your speed in mps.
This stuff really should be taught. Maybe it is.
CR.
I've made errors calculating my TOD before using my brain, how many times has my pocket calculator made them? 0. But a solid understanding and a mental check of the math confirms that.
A mental check takes as much effort as rounding and getting the answer in the first place. And if you round the numbers (for most calculations that's all you need for aviation accuracy) and think about your process, you get that added gut feeling of reasonableness to boot.
The shortcuts as described here are not really that hard. Personally, I think anyone who doesn't [want to] learn them is just lazy and unprofessional.
Capt Fathom
Metres Per second.... WTF? Do I need to know that?
Last edited by compressor stall; 3rd Jan 2013 at 22:25.
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TAS (nm per min) x crab angle = crosswind comp.
You can juggle too - Crab Angle = crosswind comp / TAS nm per min.
X/W or H/W....
30* - 90% reported
45* - 75%
60* - 50%
I still use my Jepp wizzwheel but only very rarely these days - mainly
in the sim when poofteenths matter. I'm not against the Magenta kids
using a calculator but only if it doesn't take too long and they aren't in
control (ie PNF).
Flying a 3.3* profile decent and that 1m happens to equal 3.28 ft gives
the dist required to BOD. Helps if you have an altimeter reading metres
though. More applicable to us international jocks.
You can juggle too - Crab Angle = crosswind comp / TAS nm per min.
X/W or H/W....
30* - 90% reported
45* - 75%
60* - 50%
I still use my Jepp wizzwheel but only very rarely these days - mainly
in the sim when poofteenths matter. I'm not against the Magenta kids
using a calculator but only if it doesn't take too long and they aren't in
control (ie PNF).
Metres Per second.... WTF? Do I need to know that?
the dist required to BOD. Helps if you have an altimeter reading metres
though. More applicable to us international jocks.
Last edited by Slasher; 17th Feb 2013 at 06:16.
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Interesting variation on the the automation debate. I like to think about it the same way. If the aircraft has it you should be able to use it. If your have high end automation then you should be able to operate it quickly and accurately but be able to hand fly it just as well.
Having been forced by my instructors to be able to do mental DR I am eternally grateful. There is a time and place for a calculator (mainly flight logs where accuracy counts and you have time to go heads down) but mental DR is pretty handy. The FMS is not always right and not every approach can be fully programmed to touchdown so the VNAV requires some mental backup. Thanksto my instructors who insisted on mental gross error checks my occasional cock ups have not ended in tears.
Having been forced by my instructors to be able to do mental DR I am eternally grateful. There is a time and place for a calculator (mainly flight logs where accuracy counts and you have time to go heads down) but mental DR is pretty handy. The FMS is not always right and not every approach can be fully programmed to touchdown so the VNAV requires some mental backup. Thanksto my instructors who insisted on mental gross error checks my occasional cock ups have not ended in tears.