Back in the old days when grade A at A level was only given to the top 5%, Newtonian physics was taught at an early age. For those who didn't attend those classes, Mr Newton was also to be found on the back of the long missed £1 note. In those days if you handed Mr Newton over to your friendly non-theme-pub barman, you could get 3 pints of bitter and change. So the boys and girls who were down the pub instead of going to maths classes were still very familiar with Newton, even if for different reasons.
Victor Meldrew lives.
For those of you who were still twinkles in daddy's eyes back then and so will not have heard of the fellow, Isaac Newton was a famous Brit who developed calculus (ooops, another word no longer heard in the UK education system, and the French might disagree too) and also came up with some really cool laws. These are known as Newton's Laws of Motion.
Cutting to the chase, (and I did have to look this bit up
) he said that
the acceleration of an object is directly proportional to the net force acting on it and is inversely proportional to its mass
i.e.
F=ma
From the above, and using some other knowledge of the fundamental units, you can come up with the formula
v2 = u2 + 2as
Where
v = final velocity of a body
u = initial velocity of a body
a = acceleration applied to the body
s = distance travelled by the body
(and for those recent maths A-level grade A students, 2 is a number between 1 and 3)
If initial velocity is 0 (
u=0)
v2 = 2as or
s = v2/2a
Lets assume, for an airplane moving from 0 to Vr along a runway, the net force pulling the airplane forwards is constant and airplane mass is constant, so acceleration is constant. This is not going to be 100% correct, but given the speeds and environment it will be close enough for our purposes.
Lets say our Vr is 10 m/s, and
a is 1 (so
a drops out)
s = 100/2
= 50 m
So our runway has to be 50m long in reach to a Vr of 10m/s, given a constant acceleration which we have conveniently set to 1.
How fast will be be going half way down the runway, where distance = 25m???
v2 = 2as (remember
a = 1, constant acceleration) s is now 25
v2 = 50
v = 7.1 m/s.
So we have to be at 7.1 m/s half way down the runway to be assured of reaching 10 m/s at the end.
That, my friends, is 71% of the final speed, half way down the runway.
What did I say? I said, lets
start with 75%, because that is easier to work out, and it gives a little bit of a safety margin. That's why I use it, to
start with. Actually I am far more cautious than that, because I don't want to use all available runway.
Put your own figures in, you will see that if you are not traveling at over 71% of Vr half way down the runway, you
MUST abort. Otherwise, you
WILL run off the end.
Where did I mention performance charts, altitude, temperature, grass, snow or anything else which has been brought up to argue against this rule. Those of you who think this is not a hard and fast, rigid rule should sit back and spend some time contemplating
Mr Slag may not carry much weight round here, but Sir Isaac Newton should.
Cheers