# Why does rain appears to be inclined when observed from a moving car?

1. Oct 16, 2011

### akc123

Why does rain appears to be inclined when observed from inside of a moving car?

Assume that the rain is straight.
Then the person in the moving car sees that rain is inclined and a person standing on the road sees the straight rain.

Is my observation correct? When I first saw this I thought it was because of the pressure change caused by moving car or wind.

The angle of inclination increases when the speed of the car increases.
I have attached a picture:

2. Oct 16, 2011

### Vorde

It's easier to picture this as just one rain drop falling (the effect is the same, just multiply it).

The rain drop has a downward velocity of X and a horizontal velocity of 0. Therefore when you are not moving with regard to the raindrop it moves straight down. Now imagine you are moving with a horizontal velocity of H. Now to you, your Horizontal velocity is 0 (because you are always still with regard to your own reference frame), so the rain looks like it has a horizontal velocity of -H to you, and depending on H it will look like it is slanted.

3. Oct 16, 2011

### gary350

Rain does not fall exactly straight down wind blows it in a different direction so you see rain falling at an angle. It is no different than releasing a helium balloon it never goes exactly straight up the wind blows it away too. Rain is falling at a pretty fast speed that is why you see angle streaks of rain.

Rain observed from a moving car is speed added to what you see. It is the same as driving down the road towards a loud horn the speed of the car adds to the frequency of the horn so the pitch sound like a higher frequency but when you pass the horn and your driving away suddenly the frequency of the horn sounds lower because the speed of the car moving away substracts from the speed of sound.

4. Oct 16, 2011

### Drakkith

Staff Emeritus
You're not incorrect, but I'm not sure this really applies to the OP's question. We can assume that in a near 0 wind situation the rain is falling in a nearly 0 angle direction downward. When the car is moving the drops appear to fly in at the angles shown simply because the frame of the moving car makes everything, including the rain, look like it is moving. Since the rain is also falling, aka moving towards the ground, it appears to come in at an ever increasing angle as the car accelerates.

akc123, your pictures don't show the rest of the rain that doesn't hit the car. Picture yourself standing on the sidewalk as the car goes by. You would see the rain still falling straight down. The faster the car goes the more rain hits it on the front. Now imagine yourself in a jet fighter going 1500 mph. The rain appears to be coming straight at you from the front, yet in reality it is falling slowly straight down and you are the one barreling forwards at mach 2 or so.

5. Oct 16, 2011

### jetwaterluffy

Imagine the raindrop is moving really slowly, or static. When you are in a moving car the raindrop appears to be moving towards you, but that is actually because you are moving towards it, in the same way that trees appear to be moving in the opposite direction to you if you look out of the side window.
Now go back to the situation you described. That component of the raindrop's motion still exists, except now it is moving downwards as well, so you now perceive the increase in speed as a change in angle. When the raindrop and the car are moving at the same speed, the raindrop appears to come at a 45° angle, as both the components of its velocity are equal (which means it would be possible for you to work out the terminal velocity of rain.)
For a simerlar reason, water goes up a car windscreen when you are going on a moterway in the rain, rather than down. The water is staying still, while you are going forwards, and the windscreen is tilted towards you.

6. Oct 16, 2011

### KingNothing

Think of it this way: a raindrop moving straight down and the car moving toward it at 50mph is the same as the car being still while the raindrop moves toward it (horizontally) at 50mph.

7. Oct 17, 2011

### akc123

Thanks guys.Now I have understood it.

8. Oct 17, 2011

### gary350

Your right, didn't I just say the same thing only in different way. Myth Busters proved this already. One of the experements was to have 2 people go from a building to their car in the rain. The person that walked got a lot of rain on top of their head and shoulders. The person that rain got the whole front side of them wet. It turns out the person that runs fast gets wetter. Same thing in the car the faster you go the more rain that will hit you. I read some where once that wind resistance only allows rain drops to fall at about 35 mph so if you drive a car 70 mph 2 times more rain will hit you. Its basic vector type math you can prove it on paper. If your moving fast towards the rain it makes the rain look like it is coming straight at you because it is.

9. Oct 18, 2011

### jetwaterluffy

The thing is, people often care more about their head and shoulders than the rest of their body. You would probably have to weight the "wetness" depending on which part of the body it lands on. Especially as some people wear waterproofs that don't have hoods.

10. Oct 18, 2011

### Himal kharel

It is all due to velocity of rain relative to car.
the angle of inclination is given by
tanθ=Velocity of car/Velocity of rain

11. Aug 8, 2013

### cramerk59

It is an optical illusion the rain looks vertical because it also looks like its moving torwards you when accelerating.Because when traveling at 35mph you look up in to the sky it is a foot away but 2 sec later it is 1/2 a foot away then on your windshield its hard to explain but pointblank not wind only an optical illusion

12. Aug 8, 2013

### Drakkith

Staff Emeritus
Cramerk, I can't really follow what you've said. Is it anything different than what's already been said prior to your post?

13. Dec 5, 2013

### lizarddrunk

Rain and Relativity

Hi Torrent Fans....

Well, you are all right to some extent but no one, I think, is right to the full extent (nor to be fair, will anyone be once I have finished this post.....). I preface this all with the fact that I am an anthropologist, not a physicist, nor even a meteorologist, and in the main I simply observe things and try to sort out what is going on. And I have done a couple of observations of this phenomenon which might prove interesting, though the truth is I have more questions than answers to contribute.

First, clearly - as all agree - the rain is not moving (sideways) past you at the speed it appears, you are moving past the rain at that speed. But the thing about being in a vehicle is it is like Einstein's train - inside the vehicle you do not feel you are moving because, relative to the vehicle, you are not. It is only the bystander who sees that you are moving. The rain is, to some extent, a bystander.

Ok. Fine. I am good to that point. The thing that interests me is this. I have noted that if the rain is coming down virtually horizontally - perpendicular to the ground - when I am at rest, then as I speed up in my vehicle the rain increasingly appears to be deflected in the angle it is passing my window. Now I get - as several have said - that the speed the rain appears to be moving by my window to the rear is equivalent to the speed I am actually moving forward in my car.

But my interest is not so much the apparent speed of the rain - it is the angle. I have made some fairly careful observations, though certainly not rigorous, and have found the following. At about 20 kilometres an hour (hey, give me a break, I am a Yank but I live in Papua New Guinea, so it is kilometres - and yes, the r comes before the e at the end in these parts...) the rain is no longer vertical, but appears to be coming down at an angle to the vertical of about 30 degrees. When I speed up to 40 kilometres per hour the angle increases to just about 45 degrees. So I have doubled my speed for only a 50% or so increase in angle. But then I have to speed up to right around 80 kilometres per hour to get the rain to appear to subtend an angle of 60 degrees – another doubling of speed to attain, this time, about a 30% increase in angle.

These figures may not be - are not - accurate, but I think the pattern is clear. If you plot the speed on the y axis and the apparent angle on the x axis, then the curve is asymptotic. Drakkith was right, the rain appears to be coming at an "ever increasing" angle the faster you go. But two refinements here. First, the angle does not change at a constant rate with speed (though what happens with constant acceleration is a question I will broach below). Second, the implication that if you are going 1500 mph (say 2414.016 kph) in a jet trying to evade the IRS the rain will appear to be coming "straight at you" is, I think, not accurate (and I know Drakkith was only speaking loosely here). The truth is, I am pretty certain, that as the rain goes by the window of the aircraft it will be close to horizontal, but the angle will actually only be something like 88.5 degrees or 89.15 or 89.62 to the horizontal. It will not be 90 degrees.

So that is my question. Or therein resides the nexus of my questions. What is going on here? A couple of specific questions, interlaced with some observations.

First, Why is it that the curve relating speed to angle is asymptotic? I am sure the answer is simple, but I do not know it. Second, how fast do you have to go in order for the rain to appear at a true 90 degrees to the horizon? My gut feeling is that the latter answer gets back to Einstein and the speed of light. Indeed, the whole thing feels instinctively like some relation between special and general relativity. The special relativistic aspect is that all motion is relative, and the distinct frames of reference of the stationary bystander (or the rain, were it sentient) and the person in a moving vehicle result in different perceptions. Then there is the general relativistic aspect which introduces the relation between acceleration and the angle of the rain (not to mention mass, which I just did). Under a constant acceleration what happens to the angle of the rain in equal time periods? Does acceleration at a certain rate introduce the possibility of change of angle a steady rate, as opposed to the relationship between speed and angle? In that case increased acceleration would approach, but not reach the speed of light in direct relation to the angle of the rain which would approach but not reach the horizontal.

Finally, though the rain appears to change angle as speed changes, the same cannot be said for other features in the environment. For example, houses simply appear to pass at a speed equivalent to the actual speed of the vehicle but they do not appear distorted in the vertical dimension. I have also noted when it is raining hard that strong flows of water coming off the roof of a house appear to pass rapidly, but do not appear to be distorted in the vertical. I had a lot of trouble seeing the fundamental difference between a spout of water dropping to the ground and raindrops dropping to the ground. But as I thought about this in the past few days it came to me that part of this might be a matter of distance. Could it be that if I drove past a fount of water coming off a roof at close range - say ten feet distant - that the angular effect might be apparent? I have not been able to do so without serious risk to myself and others, so the hypothesis remains untested. Perhaps someone out there in a less highly traveled area can conduct the experiment. It also occurred to me it might somehow be a matter of field and ground - does the house somehow constitute a ground that prevents the optical illusion from manifesting?

And with respect to the house, that led ineluctably to another couple of thought experiments. For instance, what would happen if we had a series of houses falling straight down from the sky at a regular rate ? Would hey would appear - as our speed increased - to be falling at an angle (again I feel instinctively that this would not happen at distance, but am less certain about if they were very close to my window). And what the the houses were suspended in the sky, say fifteen houses, one levitated on top of the other in a line perpendicular to the ground,but immobile (well, relatively...). Would they also appear to describe a slanted line if you passed them at speed? Does distance affect this?

And a final question - I note that when I look at the individual raindrops as they pass my window at speed it is not a series of horizontal raindrops arranged at an angle in relation to one another, but that, instead, each raindrop, which is actually an elongated drop of water perhaps half an inch or more in length, appears at an angle. That is, the individual drops are distorted at the same angle as the row of drops. It is the difference between A and B below (hope this comes out in the text, but I think you know what I mean....

A. I B. /
I /
I /

So the question is would those houses appear each to be distorted at an angle to the horizontal as well? And why not??

Sorry for going on, but I find this interesting and I have been thinking about this over the past few days because we have had torrential rain with plenty of time for observation. I then googled "why does the rain appear to change angles when you speed up in a car" and found this site. It has been a good discovery. Hope I haven't overstayed my welcome, but I would be interested in any reactions....

Cheers
Lizard

14. Dec 5, 2013

### voko

This is really a simple thing. It involves vectors. The velocity of rain with respect to the ground is $\vec V$. The velocity of the vehicle with respect to the ground is $\vec v$. These two vectors are perpendicular. The velocity of rain with respect to the vehicle is $\vec V - \vec v$. To visualize: $\vec V$ is an arrow pointing downward, and $\vec v$ an arrow pointing to the right; their tips are in contact. Then you can connect the "butts" of the arrows with another arrow, pointing downward and to the left; this is the velocity of the rain apparent from the vehicle.

Now, the angle. The tangent of the angle of the apparent velocity with the ground is the ratio of V and v: $$\tan \alpha = \frac V v,$$ so $$\alpha = \arctan \frac V v.$$

To simply things somewhat, let's make the velocity of the rain our unit of measure; in these units, the formula above becomes $$\alpha = \arctan \frac 1 v.$$

Attached is the plot of the angle, in degrees, against the speed of the vehicle (in units of the rain speed).

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