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How exactly can you calculate the distance between you and a thunder storm? Here's the Math!

 
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*This post is mostly me having fun practicing unit conversions for my Chem 1 class. I figured it may have some relevance to wilderness survival. I honestly used to think that each second between lightening and thunder represented 1 mile (1.6 km). This could have easily led to dangerously miscalculations--5 miles (assumed) vs 1 mile (actual distance).* Feel free to correct any mistakes or provide alternatives!

Final Results
1 mile = 5 seconds
1 kilometer = 3 seconds
0.2 miles = 1 second
0.3 kilometers = 1 second

The speed of light is 0.000621 miles/second. That means lightening is visible to distance of 1,610 miles after just one second. I think it is safe to assume that the speed of light has a negligible effect on the final calculation. We will assume that the time from the actual strike to the time it is visible to you is 0.

1 second ÷ 0.000621 miles/second = 1,610 miles

(www.weather.gov)'s speed of sound calculator says that at 40 degrees F, sound travels at 746.95 miles/hour. For miles/minute divide by 60. And for miles/second divide that by 60 again. This tells us a storm is 0.207 miles away for every 1 second of time between lighting and the sound of thunder. This means that for every 4.83 seconds counted, 1 mile of distance lies between you and the source of the strike.

746.95 miles/hour ÷ 60 minute/hour ÷ 60 seconds/minute = 0.207 miles/second

1 mile ÷ 0.207 miles/second = 4.83 second

Sources:
Speed of Light
Speed of Sound
 
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So what is it for 70 degrees?  

Does humidity affect it much?
 
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So, for us non-mathy folks, you see the light, then count the seconds and divide by 5 to get miles? Am I reading it all correctly?
 
Christopher LaRosee
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Mike Haasl wrote:So what is it for 70 degrees?  

Does humidity affect it much?



At 70 degrees its 4.7 seconds per mile, so not a huge difference.
Also high humidity will lead to faster a speed of sound, however the difference is also very small.
 
Christopher LaRosee
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Pearl Sutton wrote:So, for us non-mathy folks, you see the light, then count the seconds and divide by 5 to get miles? Am I reading it all correctly?



You are indeed. What I have outlined is more an attempt to explain why this rule is generally the case. But I suppose you could use the more precise values and a compass and map to pinpoint exactly where a storm is.
 
Mike Haasl
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Thanks Christopher!
 
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The conclusions are good, but the values and units used in the lightning calculations look a bit odd. From bitter experience, units that don't properly cancel are a major source of lost points on chemistry exams.

The speed of light is 186,000 miles per second.

A calculation of (seconds / (miles per second)) gives units of seconds^2 per mile, or "inverse acceleration".
 
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I've always wondered about mountainous terrain and the distance calculation. I currently rely on the turtle method and watch who ever I am with. A slight duck 5 miles, ears to the collar 2.5 mile ears below the collar 1 mile or closer.
 
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