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calendar   Monday - June 01, 2020

I Saw A Sign, Plus Rule Of Thumb Math

I was down in South Plainfield yesterday afternoon doing my cleaning. And the steam sanitizing. Which is a lot of slow but easy work. It doubles my time on the job site.

Anyway, I stepped outside to put some stuff back in the car, and I heard a somewhat loud rumbling sound. I recognized it immediately as a jet plane. I haven’t heard one or even seen a contrail in the sky in months.

It’s a sign of life beginning to get back to normal. Oh happy day. A very small sign; the airlines are still just about shut down. Usually there are so many jets low in the sky there that it’s noise pollution. Out where we live in Clinton, jets are these silent microdots that crawl across the clouds leaving their steam trails behind them.

South Plainfield is on the landing path for Newark airport, just 16 miles away NE. So I looked up and there was a 747 coming in low and slow on early approach, wheels not yet out and in a slight bank. Totally cool.  I held up my arm and stuck out my thumb and a bit over half my thumb covered the plane.

It was pretty close. Not right on top of me, but still, pretty close.

~~~~

Math problem: A typical 747-8 is 250 feet long. I measured that much subtending thumb as 1.5”, and my thumb was 22” from my eye. How far away was the 747?

This is not as hard as you think. It’s actually quite like the way hunters use the thickness of the crosshairs in their scopes to judge distance.

At first I figured I’d need all that SOHCAHTOA stuff from math class, along with arctan and a full featured calculator. But then I realized I should use the KISS principle, which made it much easier. A simple calculator does the job.

The angle formed by my thumb and the length from my eye - the opposite and adjacent sides of a right triangle - is the same angle as one made by the length of the airplane and it’s distance from me.

250 feet is 3000 inches.

So (using tangent’s opposite/adjacent concept) 1.5/22 = 3000/X ... 1.5 = 22*3000/X ... 1.5 = 66,000/X ... 1 = 44,000/X ... X = 44,000 inches… 44,000/12 = 3666.67 feet ... 3666.67/5280 = .69 miles.

So the jet was about 2/3 of a mile away. I can only guesstimate the vertical angle of my arm as a bit over 45°, so I’d guess the 747 was about 1/2 mile up in the air. These are really big airplanes.


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Posted by Drew458   United States  on 06/01/2020 at 09:49 AM   
Filed Under: • Fun-Stuff •  
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