Hello Beagle,
In the head. Something like this.
103kts, somewhere between 100kts and 110kts. 100kts factor 0.6. 110kts factor 0.55(the factor is the no. of nmls covered in 1 min.)
17mls,@100kts, time taken =8.5+1.7(0.1 is a 1/10 of 17) = 10.2mins.
17mls@ 110kts then 8.5+ 0.85 (0.05 is 1/10 of 0.5 which is ½ of 17 which is 8.5) = 9.3 mins.
If it takes 10 mins exactly Gspd will be 102kts.
(17 times 60/10 ie times 6=60+42=102). Use this as the base.
In the air. 10 mins=102kts. Shade over 11mins 90kts. 8.5 mins 120kts. Split the difference if accuracy is requd. Ie 10.5mins use 95kts. 9.5mins use 110kts.
Whatever the time taken, double it and add to the real time to get best ETA. if 17mls is 1/3 of the route which continues in a straight line.
Quite a good example, that shows the benefit of doing the MDR for pre-flight planning on the ground. You get an idea of the type of calculations and the sort of figures you’re using in advance, so when you come to do them in the air, you remember and recognise them. The 90kts to 120kts is a tricky area. 90kts is 2/3 or 0.66 and 120kts is 0.5 or ½ and 100kts is 0.6. In the example you gave, you used fractions. Sometimes decimals are easier, sometimes fractions are easier. Use whatever is easiest as accuracy is not paramount. Both can be used. What is required is a facility to switch between fractions and decimals and rounding up and down, something that has been lost in the calculator age.
In navigation, 60 is everywhere. Take 17 mls in 13 mins. If 17mls in 12 mins,17 times 5. If in 15 mins 17 times 4, then split the difference. But that involves three “reckonings.” For me that’s too many.
Using my method, I know that 60/13 =4.6(approx), so 17 times 4.6 = 40+28+9or 10 =78kts. Only one “reckoning”.
Although lots of nos divide into 60, the problems come from the ones that don’t. I’m not usually going to be flying a leg longer than 20mins without a pinpoint. So I’m only interested in the nos that don’t divide into 60 between 1 and 20. These are 7 8 9 11 13 14 16 17 18 19( so near to 20 it can be chucked out
Strangely the nos make an easily remembered sequence.
60/7=8.6
60/8=7.5
60/9=6.6
60/11=5.5
60/13=4.6
60/17 =3.5
As for 14,16 and 18 into 60, they are ½ that of 7,8,9, so 4.3, 3.75 and 3.3 respectively.
The benefit of committing this little table to memory is that you only have to do one multiplication in the air. It’s not super- accurate. There has been fairly liberal rounding up and down, but it meets the requirements for easier DR in the air. For any application there is always a balance between accuracy and speed. In the DR situation speed and facility get priority over accuracy, within limits.
Getting the wind vector can be done mentally but involves about 3 calculations using the 1in 60 rule and
gives the wind angle to the plane. Too much. The plastic gadgets win out on this one. Gspd +WCA, simple up down movement of protractor on Gspd scale and read-off. Simple Triangle of Velocities and very accurate. MDR thereafter, comparing what you thought you would get with what is actually happening.
I’m off to check the GPS still works and give it a chance to up-date the almanack and ephemeris. Great little things. Gives the passengers something to play with, keeps them strangely reassured as to where they are, where they’re going, and most important of all, answers the question( but only based on the current GSpd) “When are we going to get there?" Probably the mindset is "If it's on TV or something that looks like a TV it must be OK." Just a passing thought but may be not a few pilots have the same mindset.