Raindrops are wet!
2002-Jun-17, Monday 21:10![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
thorfinnThat's right, raindrops are wet. But how wet, that's the question! At various times and places, the question, "is it better to run or walk when it's raining?" has been raised... and I've never had a satisfactory answer from discussion. So, whilst in Sydney visiting the rels, the question came up again, and this time, I decided to take a physics approach to the problem.
First, we simplify the problem to something we can understand, then we frob the parameters until it looks more realistic.
So, we start by assuming a cuboidal human with a waterproof bottom side. This gives us five sides that can "get wet" to worry about... the top, the front, the back, and the left and right sides.
Next, we assume completely vertical rainfall at a constant rate. This means that if our cuboidal human is standing perfectly still, the only side that gets wet (ignoring drippage - let's also assume our initial cuboidal human is a perfect water-absorber) is the top side, and the rate is determined by how long our human stays in the rain.
Okay. Now lets play with the constraints. If our cuboidal human (OCH) moves horizontally towards the front, then OCH still picks up water on OCH's topside, at the same rate as if OCH were standing still. But what about OCH's sides? Now, if the rainfall is perfectly vertical, then OCH's front-side will be moving "into" raindrops as they fall down, and no other sides will be affected.
Since we're assuming constant speed perfectly vertical rainfall, then I think that this can be abstracted as a non-moving mist of droplets (the density of the mist being determined by the rate of downfall - faster rainfall, thicker mist)... What does that mean? That means that over the same distance, the amount of water arriving on OCH's front-side is identical, whether OCH moves fast or slow!
Whoa. Okay. But there's a third factor to consider... OCH is also warm. This means that water collected on OCH will evaporate at a certain rate... So, if OCH moves slowly, and the rainfall is light (ie, the mist is low density), water collected on OCH's front-side will evaporate as fast as it collects... and that's true of OCH's top-side as well!
Now, lets say that OCH's sides all have a certain amount of water they can collect before they become "soaked"... So, if it is raining lightly, and OCH runs fast, OCH's frontside collects a lot of water, and becomes soaked. At which point, OCH's wet on the inside, and starts to scream "I'm melting, I'm melting!". If OCH goes slowly, then the rate of evaporation vs the rate of water collecting on OCH's front is quite high, so OCH's never wet on the inside...
If, however, it's raining heavily, then OCH's better off running, because the amount of rainfall on OCH's top-side is quite high, and OCH's front-side is probably doomed to become wet no matter what.
Hrm. Okay. Now, how about constant non-vertical rainfall? What does that do to the problem? Well... if the rainfall is going in the same direction that OCH is, then OCH's in luck. OCH should move forward at the same rate (or possibly slightly faster than) the horizontal component of the rainfall's motion... How much faster depends on the rate of downfall vs the rate of collecting rain on OCH's front-side by outrunning the rain - minimising the top-side wetness by moving faster vs increasing the front-side wetness. Now, OCH's actually usually quite a bit smaller on top-side than on front-side, so that means that if there's horizontal rainfall from behind OCH, then OCH should outrun the rain, but not by very much.
What if the rainfall has a sideways component? Then that's the same as the topside... OCH can't do anything about that, but it becomes a factor in how fast to run, because the more sideways the rainfall, the faster OCH gets wet on the side, so the faster OCH should run to minimise the duration of wetting, but again, factoring in the fact that if OCH runs faster, OCH gets wetter on his front-side.
If the rain is coming from in front of OCH, then it's all bad. OCH's frontside is doomed to get soaked... Or is it? There's a solution to this! Lean forward, to minimise OCH's profile, so that OCH's topside is the one that's exposed to the rainfall... which then reduces it to the earlier problem, of topside rainfall rate vs how much to outrun the rain... That solution applies to sideways vectoring rainfall too, but OCH usually has much trouble moving forward whilst leaning sideways, so that's not very useful.
So... what's it all mean? Actually, the conclusions are quite useful! If it's not raining hard (and not blowing hard in any particular direction), then OCH's better off walking slowly, possibly with OCH's arm over OCH's head to improve the amount of of topside absorption before soaking, because the evaporation component is big enough relative to the rate of getting wet that OCH's probably going to stay mostly dry. If it is raining hard (or is blowing hard sideways), then OCH's better off running, to minimise the time spent in the hard rain, because the evaporation component is too small in comparison to the rate of wetting... and the only other slight side issue, is if OCH's very lucky, and the rainfall is coming from behind at slow enough for OCH to keep up, then OCH should try to match (and slightly overshoot) the horizontal speed of the rainfall.
Of course, OCH's probably better off carrying an umbrella and/or wearing a raincoat... but that's not as geeky as working out the problem. *grin* Oh, and just to note, the above theory matches my experiences with various rainfall.
First, we simplify the problem to something we can understand, then we frob the parameters until it looks more realistic.
So, we start by assuming a cuboidal human with a waterproof bottom side. This gives us five sides that can "get wet" to worry about... the top, the front, the back, and the left and right sides.
Next, we assume completely vertical rainfall at a constant rate. This means that if our cuboidal human is standing perfectly still, the only side that gets wet (ignoring drippage - let's also assume our initial cuboidal human is a perfect water-absorber) is the top side, and the rate is determined by how long our human stays in the rain.
Okay. Now lets play with the constraints. If our cuboidal human (OCH) moves horizontally towards the front, then OCH still picks up water on OCH's topside, at the same rate as if OCH were standing still. But what about OCH's sides? Now, if the rainfall is perfectly vertical, then OCH's front-side will be moving "into" raindrops as they fall down, and no other sides will be affected.
Since we're assuming constant speed perfectly vertical rainfall, then I think that this can be abstracted as a non-moving mist of droplets (the density of the mist being determined by the rate of downfall - faster rainfall, thicker mist)... What does that mean? That means that over the same distance, the amount of water arriving on OCH's front-side is identical, whether OCH moves fast or slow!
Whoa. Okay. But there's a third factor to consider... OCH is also warm. This means that water collected on OCH will evaporate at a certain rate... So, if OCH moves slowly, and the rainfall is light (ie, the mist is low density), water collected on OCH's front-side will evaporate as fast as it collects... and that's true of OCH's top-side as well!
Now, lets say that OCH's sides all have a certain amount of water they can collect before they become "soaked"... So, if it is raining lightly, and OCH runs fast, OCH's frontside collects a lot of water, and becomes soaked. At which point, OCH's wet on the inside, and starts to scream "I'm melting, I'm melting!". If OCH goes slowly, then the rate of evaporation vs the rate of water collecting on OCH's front is quite high, so OCH's never wet on the inside...
If, however, it's raining heavily, then OCH's better off running, because the amount of rainfall on OCH's top-side is quite high, and OCH's front-side is probably doomed to become wet no matter what.
Hrm. Okay. Now, how about constant non-vertical rainfall? What does that do to the problem? Well... if the rainfall is going in the same direction that OCH is, then OCH's in luck. OCH should move forward at the same rate (or possibly slightly faster than) the horizontal component of the rainfall's motion... How much faster depends on the rate of downfall vs the rate of collecting rain on OCH's front-side by outrunning the rain - minimising the top-side wetness by moving faster vs increasing the front-side wetness. Now, OCH's actually usually quite a bit smaller on top-side than on front-side, so that means that if there's horizontal rainfall from behind OCH, then OCH should outrun the rain, but not by very much.
What if the rainfall has a sideways component? Then that's the same as the topside... OCH can't do anything about that, but it becomes a factor in how fast to run, because the more sideways the rainfall, the faster OCH gets wet on the side, so the faster OCH should run to minimise the duration of wetting, but again, factoring in the fact that if OCH runs faster, OCH gets wetter on his front-side.
If the rain is coming from in front of OCH, then it's all bad. OCH's frontside is doomed to get soaked... Or is it? There's a solution to this! Lean forward, to minimise OCH's profile, so that OCH's topside is the one that's exposed to the rainfall... which then reduces it to the earlier problem, of topside rainfall rate vs how much to outrun the rain... That solution applies to sideways vectoring rainfall too, but OCH usually has much trouble moving forward whilst leaning sideways, so that's not very useful.
So... what's it all mean? Actually, the conclusions are quite useful! If it's not raining hard (and not blowing hard in any particular direction), then OCH's better off walking slowly, possibly with OCH's arm over OCH's head to improve the amount of of topside absorption before soaking, because the evaporation component is big enough relative to the rate of getting wet that OCH's probably going to stay mostly dry. If it is raining hard (or is blowing hard sideways), then OCH's better off running, to minimise the time spent in the hard rain, because the evaporation component is too small in comparison to the rate of wetting... and the only other slight side issue, is if OCH's very lucky, and the rainfall is coming from behind at slow enough for OCH to keep up, then OCH should try to match (and slightly overshoot) the horizontal speed of the rainfall.
Of course, OCH's probably better off carrying an umbrella and/or wearing a raincoat... but that's not as geeky as working out the problem. *grin* Oh, and just to note, the above theory matches my experiences with various rainfall.
