Mental maths - tips, tricks and shortcuts
One I use for percentages (especially multiples of 10%) is to divide by 10 and then multiply by whatever number you need to get the right percentage.
I.e. 20% of 20 = 20/5=4 nice and easy. but 20% of 17.8 I would find too hard to just divide by 5.
So I do 17.8/10= 1.78 (10%) x2= 3.56.
Works for multiples of 5% as well. you just do the same thing to the 10% level below and then add half of the original figure.
I.e. 35% of 56= 5.6x3=16.8 (30%) + 2.8 (half of 10%)=19.6.
I.e. 20% of 20 = 20/5=4 nice and easy. but 20% of 17.8 I would find too hard to just divide by 5.
So I do 17.8/10= 1.78 (10%) x2= 3.56.
Works for multiples of 5% as well. you just do the same thing to the 10% level below and then add half of the original figure.
I.e. 35% of 56= 5.6x3=16.8 (30%) + 2.8 (half of 10%)=19.6.
Or you can round a bit to make it easier -
35% of 56:
Do 35% of 60, which is 3 and a half times 6, ie 21. Take a little bit off because 56 is a bit less than 60, call the answer 20.
Or to be slightly more scientific, 35% of 60 is 21.
56 is 4 less than 60, or about 6% less (two-thirds of 10%).
So my answer should also be two-thirds of 10% less, or 21 minus 1.4, which is 19.6.
35% of 56:
Do 35% of 60, which is 3 and a half times 6, ie 21. Take a little bit off because 56 is a bit less than 60, call the answer 20.
Or to be slightly more scientific, 35% of 60 is 21.
56 is 4 less than 60, or about 6% less (two-thirds of 10%).
So my answer should also be two-thirds of 10% less, or 21 minus 1.4, which is 19.6.
Reciprocal headings, add 200 minus 20 or vise versa or add 2 minus 2 to keep it simple
150 add 200 = 350 minus 20 = 330
300 minus 200 = 100 plus 20 = 120
300 minus 200 = 100 plus 20 = 120
What's wrong with.....
150+180=330 and 300-180=120!
Some of these work-arounds are more complicated than the original!
Sorry, Wally.
Gotta disagree here (partially).
I am seeing WAY too much of students that can't even do simple addition without a calculator. The overreliance on this automation is the problem. Don't laugh, but I have actually seen finger counting to add two single digit numbers.
WHAT THE F
CK??!!??
Not saying everyone finds multiplying two double digit numbers easy, but practise and using unfcukupable tools are a starting point.
Did I mention practise?
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...? Notice how it gets easier with time?
Because you practise! Being able to get these answers without having to take your socks off has gotta make things easier when your workload has gone ballistic.
Not trying to drift the thread here, but seeing similar things with many AFR navexs where GPS has taken over.
Gotta disagree here (partially).
I am seeing WAY too much of students that can't even do simple addition without a calculator. The overreliance on this automation is the problem. Don't laugh, but I have actually seen finger counting to add two single digit numbers.
WHAT THE F
CK??!!??Not saying everyone finds multiplying two double digit numbers easy, but practise and using unfcukupable tools are a starting point.
Did I mention practise?
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...? Notice how it gets easier with time?
Because you practise! Being able to get these answers without having to take your socks off has gotta make things easier when your workload has gone ballistic.
Not trying to drift the thread here, but seeing similar things with many AFR navexs where GPS has taken over.
Join Date: Dec 2003
Location: The cloud
Posts: 409
Likes: 0
Received 0 Likes
on
0 Posts
Always laughed at the time to decimal place card in the cockpit. Till I used it a few times... Oh how quickly we build reliance on something.
Seriously 0.1= 6 mins IS easy, but after 16 hr split duty have to confess, out comes the app, calculator and socks off...
Gone back to refusing to use tools and cards for simple arithmetic and low and behold, I can figure stoof out again. Amazing!
Even to the point that ops staff were simply amazed when I figured out the fuel in kg just by taking off 20%... wow no fms, calculator, app, whiz wheel or toes required.
So best tip, trick and shortcut? Put down the calculator! Pick up the pen!
Seriously 0.1= 6 mins IS easy, but after 16 hr split duty have to confess, out comes the app, calculator and socks off...
Gone back to refusing to use tools and cards for simple arithmetic and low and behold, I can figure stoof out again. Amazing!
Even to the point that ops staff were simply amazed when I figured out the fuel in kg just by taking off 20%... wow no fms, calculator, app, whiz wheel or toes required.
So best tip, trick and shortcut? Put down the calculator! Pick up the pen!
Join Date: Mar 2011
Location: East
Posts: 186
Likes: 0
Received 0 Likes
on
0 Posts
Then pen works fine until you forget to carry a 1 and cause a mess as a result.
Then you get back to technology to fill out the occurrence report which will no doubt be an online form.
There is a reason technology has become such a reliance in aviation. Not such a problem calculating a 1:60 in a GA aircraft.. your visual and can probably get close enough to see the destination.
Doing the math mentally, getting it wrong and not loading enough fuel in the 767 will land you in Gimli.
Then you get back to technology to fill out the occurrence report which will no doubt be an online form.
There is a reason technology has become such a reliance in aviation. Not such a problem calculating a 1:60 in a GA aircraft.. your visual and can probably get close enough to see the destination.
Doing the math mentally, getting it wrong and not loading enough fuel in the 767 will land you in Gimli.
Join Date: Jun 2004
Location: Mydadsbag
Posts: 1,113
Likes: 0
Received 0 Likes
on
0 Posts
I just love the idea that reading little numbers on an electronic calculator is bad airmanship. Apparently reading smaller numbers on a whizz wheel is not!
Get with the times, encourage common sense, if someone is fast and safe using any technique, then rather than "throwing stuff into the baggage hold" take some notes yourself, you might learn something!
Bbbbbbbbbbbbbbbzzzzzzzzbzbzbzzzzzzbzzbzzz
Get with the times, encourage common sense, if someone is fast and safe using any technique, then rather than "throwing stuff into the baggage hold" take some notes yourself, you might learn something!
Bbbbbbbbbbbbbbbzzzzzzzzbzbzbzzzzzzbzzbzzz
Join Date: Aug 2011
Location: QLD
Age: 50
Posts: 44
Likes: 0
Received 0 Likes
on
0 Posts
Good o'l Calculators
Got to agree on mental maths.
Make it Happen Captain, agree with the mental stuff and whizz wheel at student level/flying school ops, however outside of GA, the calculator is your best pal.
Example..
If you do 8 sectors there is a "Deck log/ Flight log" to be filled out for each sector and it has to be crunched quickly, as the turn around can be 30 mins.. These compile of converting pounds to kg- litres to kg- minutes to dec. points, along with other calculations.
A calculator is a must, No guestimations here. It is also stated in Part B/SOP's, that a calculator is to be used for the Deck logs/MEL's.
ANOTHER THING GUYS/GIRLS.....GENERATION Y ARE A DIFFERENT BREED WITH REGARDS TO TECHNOLOGY....CALCULATORS RULE FOR THEM. I notice some here mentioned "batteries"....geez you must be a baby boomer or Gen x....
Solar power and battery combination along with pocket size/ compact units that fit right in your right pocket of your shirt,if you lose it, there is also a iPhone....
Anyhow, as mentioned still got to love mental maths for TOD points... Oops, the FMC does it for me....
Make it Happen Captain, agree with the mental stuff and whizz wheel at student level/flying school ops, however outside of GA, the calculator is your best pal.
Example..
If you do 8 sectors there is a "Deck log/ Flight log" to be filled out for each sector and it has to be crunched quickly, as the turn around can be 30 mins.. These compile of converting pounds to kg- litres to kg- minutes to dec. points, along with other calculations.
A calculator is a must, No guestimations here. It is also stated in Part B/SOP's, that a calculator is to be used for the Deck logs/MEL's.
ANOTHER THING GUYS/GIRLS.....GENERATION Y ARE A DIFFERENT BREED WITH REGARDS TO TECHNOLOGY....CALCULATORS RULE FOR THEM. I notice some here mentioned "batteries"....geez you must be a baby boomer or Gen x....
Solar power and battery combination along with pocket size/ compact units that fit right in your right pocket of your shirt,if you lose it, there is also a iPhone....Anyhow, as mentioned still got to love mental maths for TOD points... Oops, the FMC does it for me....
Join Date: Jan 2009
Location: Australia
Posts: 201
Likes: 0
Received 0 Likes
on
0 Posts
Jeez, and I thought mental maths was supposed to make things simpler and easier... some of the stuff in this thread makes my brain hurt
Clock code for xwind, TOD, RoD etc., sure, but fuel conversions, planning etc., I'll stick with a calculator thanks - why make things harder than they have to be??
Clock code for xwind, TOD, RoD etc., sure, but fuel conversions, planning etc., I'll stick with a calculator thanks - why make things harder than they have to be??
Join Date: Sep 2003
Location: S37.54 E145.11
Posts: 639
Likes: 0
Received 0 Likes
on
0 Posts
Years ago when I was in the old CAA, I was checking out a new (young) guy for a rating on a certain sector. One aircraft this guy was responsible for was tracking between two reporting points that were 119 nm apart and the pilot's ETI for the route segment was 60 mins. Casually I ask the guy I was checking what was the pilot's approximate groundspeed.
To my surprise he reaches for a calculator! I still shake my head at that one.
Surely there must still be a need for some mental maths ability!
To my surprise he reaches for a calculator! I still shake my head at that one.
Surely there must still be a need for some mental maths ability!
There'll always be a place for it.
I like new technology that makes life easier, but I don't think I've ever owned or used an electronic device that didn't malfunction in some way at some time.
Knowing you can deal with loss of gear (GPS being the most notable one these days I think) without totally losing the plot is good.
Plus, it's just good airmanship to be able to check if the automation is telling you bull****, be it because of equipment or operator failure, or both.
I like new technology that makes life easier, but I don't think I've ever owned or used an electronic device that didn't malfunction in some way at some time.
Knowing you can deal with loss of gear (GPS being the most notable one these days I think) without totally losing the plot is good.
Plus, it's just good airmanship to be able to check if the automation is telling you bull****, be it because of equipment or operator failure, or both.
Join Date: May 2008
Location: Somewhere
Posts: 283
Likes: 0
Received 0 Likes
on
0 Posts
Jeez, and I thought mental maths was supposed to make things simpler and easier... some of the stuff in this thread makes my brain hurt
Clock code for xwind, TOD, RoD etc., sure, but fuel conversions, planning etc., I'll stick with a calculator thanks - why make things harder than they have to be??
Clock code for xwind, TOD, RoD etc., sure, but fuel conversions, planning etc., I'll stick with a calculator thanks - why make things harder than they have to be??
Its not that hard to remember that 100lbs of JetA is almost 60 litres.
For example if i want 500lbs ill be ordering about 300 litres, and if its been ordered for me if all of a sudden i saw 400l or 200l I know something somewhere isnt quite right for whatever reason.
That's not "harder than they have to be". It's actually quicker than removing calc/phone from pocket and punching in 500 / 1.76 = into it!
Sure we arent trying to sin/cos/tan angles or anything like that so some things are irrelevant, but mental maths is very useful to dummy-check figures in all aspects of flying or at least get a rough estimate to get things going and work out an absolute later.
Join Date: Mar 2008
Location: Why oh why would I wanna be anywhere else?
Posts: 1,305
Likes: 0
Received 1 Like
on
1 Post
To my surprise he reaches for a calculator! I still shake my head at that one.
I suspect that afterwards, when calmed down, there would have been a forehead slapping moment in private.
But, of course, you've never been in that situation have you? I just LOVE empathetic examiners
Join Date: Jul 2005
Location: Queensland
Posts: 686
Likes: 0
Received 0 Likes
on
0 Posts
Sorry-I can't help myself. I always do a rough mental calculation to assure myself that the box of silicon chips probably gave me the correct answer. It's too easy to hit for example the x button when you really meant to divide. So if I'm adding 256 L of Avgas and I need to calculate the added weight I mentally note it should be less than 256kg but more than half of 256kg. I then multiply 256 by 0.7 and arrive at 179.2 so it's probably correct. If I arrive at 365.7 I know I've made a mistake,in this case divided instead of multiplying.
Two more handy rule of thumbs.
For 75% power use the rule of 48. MP in Inches plus RPM hundreds will be pretty close to 75% power if they total 48 eg 24 inches MP plus 24 hundred revs is about 75% power so is 23plus 25 or 21 plus 27
For TAS use 2% of the IAS X altitude in thousands and then add this result to the IAS
eg Indicating 135 knots @ 9500 feet you get 2% of 135 = 2.7 X 9.5 = 25.65 plus 135 =160.65 knots. This doesn't allow for temperature effects but it's pretty close to right.
Cheers RA
Two more handy rule of thumbs.
For 75% power use the rule of 48. MP in Inches plus RPM hundreds will be pretty close to 75% power if they total 48 eg 24 inches MP plus 24 hundred revs is about 75% power so is 23plus 25 or 21 plus 27
For TAS use 2% of the IAS X altitude in thousands and then add this result to the IAS
eg Indicating 135 knots @ 9500 feet you get 2% of 135 = 2.7 X 9.5 = 25.65 plus 135 =160.65 knots. This doesn't allow for temperature effects but it's pretty close to right.
Cheers RA
Join Date: Sep 2003
Location: S37.54 E145.11
Posts: 639
Likes: 0
Received 0 Likes
on
0 Posts
sisemen:
Don't fret sisemen, the young guy still passed the check OK because, despite using the calculator, he still gave me the correct answer and, apart from that, I also appreciated he was under some level of stress at the time due to a heavy sector workload and the fact that he was being checked. He performed well given all the circumstances, so I WAS EMPATHETIC.
But you're right there was a forehead slapping moment after the event.
But, of course, you've never been in that situation have you? I just LOVE empathetic examiners
But you're right there was a forehead slapping moment after the event.
Join Date: May 2008
Location: Australia
Posts: 4
Likes: 0
Received 0 Likes
on
0 Posts
Join Date: Feb 2012
Location: Honah Lee
Posts: 23
Likes: 0
Received 0 Likes
on
0 Posts
To nail a 3 degree glideslope, use RoD of 5 x groundspeed! (Because a 3 degree slope is a 5% gradient). Simple, but effective.