Cliff notes at bottom.
Ok, I just spent a couple hours on this damn intensive math analysis, that actually is probably spot on, but no one will read or pay any attention to.
Bastards.
Good thing I'm doing this mostly for me.
(lightning striking the open ocean)
Whales have been around 50 million years.
A rough scan of all the
whale species, including toothed whales suggests at any given time (until recently) there might be 10 million whales floating around in the ocean.
http://www.answerbag.com/q_view/505477 : The most common is the minke whale. The most common toothed whale is the sperm whale. (Both estimated at about a million at one time.)
[img]http://www.*********************/uploads/f57635e6fb.gif[/img]
(lightning strikes per year per square KM)
http://askville.amazon.com/lightning...uestId=3738117
Based on this chart, lightning is certainly less common at sea, but it's not unheard of. Also it's more common near the coasts, which is also where whales live. (I don't have a source on this but I think it's common sense to assume there are more whales close to coasts than out in the middle of the open ocean - also based on documentaries and reading up on some species some species - please refute if wrong). So just pure eyeball rough guess I'd say the number of lightning strikes per sq. km per year within 100 KM of the coast is 7.
Remember it's not that important to get it completely accurate, just to be somewhere in the order-of-magnitude ballpark.
So to figure out the total ocean area within 100 KM of a coast is a little tricky. We can't just multiple the coastline length (587k KM) * 100 because all the crags and right turns will be magnified. So lets just wild-ass guess and say the earth has about 2x its tropical circumference and 5x its longitude in 100 KM wide strips of coastline (look at the map). That is 2*37k km + 5*20k km = 174k KM of coastline (ironing out the small crags). This is inline with our 587k miles with crags, so that's good.
So we have 174k * 100 KM wide = 17 million square KM of coastal whale habitat.
So let's just say 1 whale per square KM. That works out nicely. It also passes the sanity check with what we know about whales and their need for huge habitats to roam around in.
So we have our one whale swimming around in his 1 KM of habitat. What are his odds of getting hit in a given year? We know from previous reading in this thread that the lightning pretty much has to strike him directly, as any water will conduct electricity away from him. Although I would think if it hit his blow hole spout, the electricity would actually conduct right into him. But for our purposes now let's just assume the whale gets hit if the lightning happens to strike right on his body while he's surfaced.
From reading around it looks like whales breathe about every 5 minutes, but can stay under for 30 when they need to. Let's assume a whale stuck in a lightning storm is trying to breathe as little as possible so staying under for 30. I think his whole surface, spout, breathe, dive sequence takes about 5-10 seconds, depending on the size of the whale. Although the last 5 seconds of that might be only the tail out of the water. And a strike on the tail may not kill the whale. So let's say 5 seconds.
Another wild-assed guess, but let's say the average exposed surface of a breathing whale is about half the size of the top of a bus. (Minke and Sperm whales are both pretty big, and they're the most populous - blue whales can be longer than 2 buses). So we'll say about (7.5x2) 15 sq meters.
Ok, now we're getting somewhere. Remember we have 7 lightning strikes per year over 1 sq. KM (= 1 million sq. meters). So let's break down the odds of our one whale getting struck by one of those 7 lightning strikes in a given year:
(5 seconds / 30 minutes) = .28% = percent of time whale is at the surface.
(15 / 1 million) = .000015 = odds 1 lightning strike hits the area of the ocean that the whale is swimming in.
.000015 * .28% = 4.16667E-08 = odds of whale being at surface when that strike hits.
4.16667E-08 * 7 = 2.91667E-07 = odds of that one whale getting hit in a given year.
So obviously pretty small. But lets look at the whole population, and over time.
2.91667E-07 * 17 million (sq KM of whale habitat) = 4.96 whales getting hit on the top of their bodies every year on average.
So multiply that * 50 million and lol. You have 250 million whales dying of lightning strikes over all time.
It's very possible my math is off by even an order of magnitude on the whale surface area, or coastal habitat, or time at the surface, or how well the avoid electrical storms, or whale fatality from lightning strikes, etc. BUT the point is, you're still going to have a crapton of whales hit by lightning in the history of whales.
The only caveat is if there's something about their bodies that make them less likely to be hit than the ocean, or maybe if they're wet the electricity just shoots around their bodies. But I think you could also argue their spout could act like a giant lightning rod and draw the lightning right into their bodies. Who knows on that.
cliff notes: Point is by sheer odds of exposed surface area, whales should have been struck at least a few million times in history.
Last edited by suzzer99; 03-27-2009 at 02:03 PM.