"As the walker begins to move, she or he receives raindrops that would have fallen in front, while missing the drops that now fall behind. This creates a balance, and ultimately, the amount of rain received on horizontal surfaces remains unchanged, regardless of the walking speed."
This is wrong. The back, stationary or moving forward does not receive rain. When stationary, the top receives rain(ideal model). When moving forward, the front AND the top receive rain. I don't see the balance they are claiming.
This is integrating over a distance, not a time. If you stay stationary you never get to your destination and get an infinite amount of rain (and the question is just ill posed).
If you move with even a tiny forward velocity then you'll start getting a few raindrops on your front. As you go faster, you get more rain per second on your front but spend less time in the rain.
Likewise the minimum amount of rain you could catch would only be on your front from moving at an infinite speed. You’d leave behind a tunnel of missing raindrops in the shape of your profile along your path.
As you move slower or faster you approach one limit or the other.
I recall even as a naive teenager with a basic understanding of calculus it was clear to me that their initial conclusion wasn’t consistent with theory.
All of this assumes the rain is falling perfectly vertically. Some trigonometry will show that in the case of a tailwind, where the rain is at your back, a scenario is possible where there is a finite speed beyond which going faster will cause you to intersect more raindrops, rather than fewer. Calculating the precise numbers is left as an exercise for the reader.
First of all, sort of bizarre for people to get caught without any rain gear. Don't you folks read the forecasts? But it's true: I see 90% of the pedestrians outside without any rain gear when it starts raining. I suppose they may be foreigners, students, homeless, or just don't really care about a little moisture. Personally I like to pack my coat whenever there's a slight chance. I had a few unpleasant episodes where I was dressed, business casual, stood at a bus stop and got soaked, with no shelter.
Anyway, I prefer to frolic and dance in the rain. It's so rare around here, and seldom so cold that I'd want to escape it. I love it when rain comes to the desert. It's a majestic thing. Although, our monsoons often come with a heaping dose of dust storms, which are best avoided. That's why I'm keeping a goodly supply of dust masks by the door!
Weather is, at least in my part of the world, pretty unpredictable.
I’ve left for outdoor activities in clear skies and sun, and within 30 minutes been standing in a thunderstorm, being pelted with hail, which was strong enough a tornado formed a few KMs away.
On the flip side, they can forecast thunderstorms every night for a week and it never rains.
I would have to carry rain gear everywhere, and it’s easier to just get wet. I am waterproof, after all.
Honestly, from the outdoorsy type of hiking apparel I've invested in during the past few years, most of my casual clothing is fairly waterproof, and I don't need to worry much about incidental rain on me.
However, if I'm dressed for church, with a button-down cotton shirt, slacks, and a matching hat, well I'd better take measures to protect that.
It's really weird in my urban environment, where it is simply assumed that everyone owns a private vehicle, parks in the parking lot, and drives around in a climate-controlled, dry, private bubble. Nobody in their right mind walks into church off the streets!
When I grew up in CA, my grandparents had a home designed by an architect from the Midwest, and it showed. One of its features was a "Mud Room" on the side: a private entrance for family and close friends only, where folks could don/doff their raincoats, snow gear, muddy boots and other stuff, leave it in there, and enter the house without tracking it all inside. Buildings in Phoenix simply don't have those amenities. They don't even have hatracks or coatracks here: you just leave it in your car!
This behavior may be a result of the climate. There’s several months where I live where the daily chance of rain falls between 20-40%, and it does rain on about a fifth to a third of those days… but the other days I have to give up bag space for an umbrella, for nothing! So I usually won’t carry rain gear unless the rain is obvious and obviously heavy (dark clouds and high winds, for instance, versus simply being overcast) or there’s some special thing where I must arrive dry (date, client meeting, the like)
That explains it. If it's rare where you are it's probably fairly forecastable. Try living somewhere with regular rain, like the UK, and you'll quickly learn that it's hard to predict and forecasts don't count for much.
I live in the Pacific Northwest, it’s always going to rain, but it won’t be much. So I don’t care if my sweatshirt gets a little moist. If it’s raining when I walk out the door, I’ll grab a jacket. Otherwise, meh, I won’t melt if I get caught in 30 minutes of drizzle.
And you live in the desert? I wouldn’t check the forecast, either. If I get wet, I’ll dry within five minutes of the sun coming out.
I’m not claiming anyone is dainty for packing a rain jacket, as I understand work clothes and the like, and I don’t like getting wet, either. But understand that some folks just don’t care all that much if they get caught out.
"As the walker begins to move, she or he receives raindrops that would have fallen in front, while missing the drops that now fall behind. This creates a balance, and ultimately, the amount of rain received on horizontal surfaces remains unchanged, regardless of the walking speed."
This is wrong. The back, stationary or moving forward does not receive rain. When stationary, the top receives rain(ideal model). When moving forward, the front AND the top receive rain. I don't see the balance they are claiming.
This is integrating over a distance, not a time. If you stay stationary you never get to your destination and get an infinite amount of rain (and the question is just ill posed).
If you move with even a tiny forward velocity then you'll start getting a few raindrops on your front. As you go faster, you get more rain per second on your front but spend less time in the rain.
Likewise the minimum amount of rain you could catch would only be on your front from moving at an infinite speed. You’d leave behind a tunnel of missing raindrops in the shape of your profile along your path.
As you move slower or faster you approach one limit or the other.
I just remember watching a Mythbusters episode where they concluded that walking kept you more dry.
Google is saying they re-did the test and reversed their conclusion. New conclusion was running is better.
I recall even as a naive teenager with a basic understanding of calculus it was clear to me that their initial conclusion wasn’t consistent with theory.
https://www.youtube.com/watch?v=HtbJbi6Sswg
TL;DW: "It's better to walk than to run in the rain."
All of this assumes the rain is falling perfectly vertically. Some trigonometry will show that in the case of a tailwind, where the rain is at your back, a scenario is possible where there is a finite speed beyond which going faster will cause you to intersect more raindrops, rather than fewer. Calculating the precise numbers is left as an exercise for the reader.
This predicament is the Richard Feynman Sprinkler of urban living. Use an umbrella.
Obviously if you walked at a snails pace, even the lightest rain would get you soaked.
Mythbusters did an episode on this.
First of all, sort of bizarre for people to get caught without any rain gear. Don't you folks read the forecasts? But it's true: I see 90% of the pedestrians outside without any rain gear when it starts raining. I suppose they may be foreigners, students, homeless, or just don't really care about a little moisture. Personally I like to pack my coat whenever there's a slight chance. I had a few unpleasant episodes where I was dressed, business casual, stood at a bus stop and got soaked, with no shelter.
Anyway, I prefer to frolic and dance in the rain. It's so rare around here, and seldom so cold that I'd want to escape it. I love it when rain comes to the desert. It's a majestic thing. Although, our monsoons often come with a heaping dose of dust storms, which are best avoided. That's why I'm keeping a goodly supply of dust masks by the door!
Weather is, at least in my part of the world, pretty unpredictable.
I’ve left for outdoor activities in clear skies and sun, and within 30 minutes been standing in a thunderstorm, being pelted with hail, which was strong enough a tornado formed a few KMs away.
On the flip side, they can forecast thunderstorms every night for a week and it never rains.
I would have to carry rain gear everywhere, and it’s easier to just get wet. I am waterproof, after all.
Honestly, from the outdoorsy type of hiking apparel I've invested in during the past few years, most of my casual clothing is fairly waterproof, and I don't need to worry much about incidental rain on me.
However, if I'm dressed for church, with a button-down cotton shirt, slacks, and a matching hat, well I'd better take measures to protect that.
It's really weird in my urban environment, where it is simply assumed that everyone owns a private vehicle, parks in the parking lot, and drives around in a climate-controlled, dry, private bubble. Nobody in their right mind walks into church off the streets!
When I grew up in CA, my grandparents had a home designed by an architect from the Midwest, and it showed. One of its features was a "Mud Room" on the side: a private entrance for family and close friends only, where folks could don/doff their raincoats, snow gear, muddy boots and other stuff, leave it in there, and enter the house without tracking it all inside. Buildings in Phoenix simply don't have those amenities. They don't even have hatracks or coatracks here: you just leave it in your car!
This behavior may be a result of the climate. There’s several months where I live where the daily chance of rain falls between 20-40%, and it does rain on about a fifth to a third of those days… but the other days I have to give up bag space for an umbrella, for nothing! So I usually won’t carry rain gear unless the rain is obvious and obviously heavy (dark clouds and high winds, for instance, versus simply being overcast) or there’s some special thing where I must arrive dry (date, client meeting, the like)
> It's so rare around here
That explains it. If it's rare where you are it's probably fairly forecastable. Try living somewhere with regular rain, like the UK, and you'll quickly learn that it's hard to predict and forecasts don't count for much.
No, I don't read the forecasts. I take an umbrella if it looks like rain outside when I leave home. I guess I just live on the edge.
It changes often enough that the sky is all I care to heed most of the time. Unless I'm planning an event.
I live in the Pacific Northwest, it’s always going to rain, but it won’t be much. So I don’t care if my sweatshirt gets a little moist. If it’s raining when I walk out the door, I’ll grab a jacket. Otherwise, meh, I won’t melt if I get caught in 30 minutes of drizzle.
And you live in the desert? I wouldn’t check the forecast, either. If I get wet, I’ll dry within five minutes of the sun coming out.
I’m not claiming anyone is dainty for packing a rain jacket, as I understand work clothes and the like, and I don’t like getting wet, either. But understand that some folks just don’t care all that much if they get caught out.
Running gets you to your destination in much less time than walking the same distance, obviously you'll probably arrive less wet.