Welcome one, welcome all to perhaps the most pointless blog you’ve ever read. Do you really need to know what the blade-tip velocity of the Tesla Cybertruck’s humongous windshield wiper is? No. It’s entirely useless info. And yet, after driving a Cybertruck yesterday and activating those wipers via a steering wheel button, I had to know. I just had to. And because I wasted a couple of minutes on these calculations, I implore you all to waste a couple of minutes reading about my waste of a couple minutes.
Ah the Tesla Cybertruck. It’s a weird machine that you’re all tired of reading about. But I got to drive one for the first time recently (review incoming!) and you know what? It was flawed; deeply, deeply flawed. But also cool. Deeply, deeply cool. It honestly spends far too much time trying to be cool, to the point that some of its features that are billed as “novel” actually just make the truck worse than it needs to be. But more on that later; that’s actually somewhat useful/insightful — this article you’re now reading is nothing of the sort. It’s pointless. It’s about the front wiper.
The front wiper on the Tesla Cybertruck is 62 inches long. That’s over five feet.
Over Five Feet. I have friends who are shorter than the Tesla Cybertruck’s windshield wiper.
My mom is shorter than the Tesla Cybertruck’s windshield wiper.
Upon activating the wiper, the first thing I thought was: “Damn, this thing swipes pretty fast. And given how long it is, that probably means it’s got a high blade-tip velocity.” Yes, it’s a curiosity I often have with rotating objects; I recently did a quick calculation of how fast the tips of wind turbines are moving. They appear to be rotating so slowly, but if you count — one Mississippi, two Mississippi — how long it takes for them to make one revolution, and you know the length of a wind turbine (they’re quite long), you realize that the tips of those blades are doing, like, 100 mph. Man I’d hate to get struck by that as a bird; unless I were traveling at 99.5 mph in the same direction, I suppose.
Anyway, let’s bring this back to the Cybertruck.
Since I know the length of the wiper, I have one of the two ingredients I need in the equation:
v = r * omega
In this equation, v is velocity in meters per second (I’ll convert that to MPH for y’all non-Metric folks). That’s what I’m solving for. r is the radius — i.e. the distance from the center of rotation to wherever we want the velocity (in our case, at the very end of the wiper, where velocity is maximized — this distance should be in meters when running this calculation). And omega is the wiper’s angular velocity in radians per second.
So we have r; it’s 62 inches, which is 1.58 meters. Now to get v, we need to find Omega; how do we do that? Well, this wiper is essentially rotating about its pivot point at the bottom of the A-pillar. The wiper is doing an approximately 90-degree sweep, so that’s a quarter of a rotation or — and this is more important — pi/2 radians.
By the way, if you want to convert degrees of rotation into radians, just have a handy dandy unit circle nearby:
I dare not interject some actually useful information into a blog that I promised would be pointless, so I won’t get into unit circles too much, but here are the basics: It’s a circle with a radius of 1 (unitless). You start labeling radians of rotation from the right side of the circle going counterclockwise, with pi/2 radians coming at 90 degrees (where the circle’s Y-coordinate is one and X is zero), pi coming at 180 degrees (-1, 0), 1.5 pi (3pi/2) coming at 270 degrees (0, -1), and 2pi being an entire rotation that brings you back to (1,0).
Just memorize this circle, and you’ll know that to convert from degrees to radians or vice versa, you just have to know that 90 degrees is pi/2 radians. Or 180 degrees is pi radians. Or 270 degrees is 3 pi/2 radians. Or 360 degrees is 2pi radians. It’s just a proportion.
The real utility of the unit circle is related to trigonometry. The unit circle’s coordinates (labeled above) represent the cosine and sine of whatever angle we’re discussing. So if we want to know what the sine of 30 degrees is, we memorize our unit circle and realize that 30 degrees — which is pi/6 — has coordinates (sqrt(3)/2, 1/2). Since the Y-coordinate on the unit circle is the sine coordinate, we know that sin(30)=1/2. That’s some useful stuff, there.
Crap, I just wrote useful stuff in this blog.
Anyway, let’s make up for that by finalizing this whole windshield wiper-tip velocity calculation. I had our video editor, the inimitable Erica Lourd, analyze the frame-rates of my video to see how long it took for the Cybertruck’s wiper to make its full sweep, which I’m estimating is a 90-degree sweep (that seems close). She seemed thrilled by this request:
She found that it took about 20 frames for the wiper to make a 90-degree wipe (she checked both up and down). Since I was shooting at 30 frames per second, this means it took 2/3 of a second for the wiper to do 90 degrees.
So how do I get Omega? Well, first, we’ve established that 90 degrees is pi/2 radians. So we just need the time component, since Omega is in radians per second. So we divid pi/2 by 2/3, and we arrive at: 2.36 radians per second.
So let’s solve v = r*Omega. r is 62 inches in meters, which is 1.57m. Multiply that by 2.36 radians/s and we end up with 3.7 meters per second. That’s equivalent to 8.3 miles per hour.
But I had a concern. If you look at my initial video, that wiper is squeaking quite a bit. It’s clear that it’s not lubricated properly; luckily, I found this great clip by YouTuber Alex On Autos:
He sprayed the Cybertruck’s glass with deionized water, and you can see that thing is moving. He even compared its speed to that of the Ford F-150 Lightning’s, and it appears that they move at roughly the same speed, it’s just that the Tesla pauses for longer.
Anyway, in this 60-frame-per-second video, Erica excitedly determined, the wiper took 28 frames to sweep its approximately 90 degree sweep. So that’s 28/60 seconds, which is .47 seconds. That’s a bit quicker than my video’s 2/3 of a second. So to calculate the blade-tip velocity, we still need Omega, which is pi/2 divided by .47 = 3.34 radians per second. Pop that into v = r * Omega, and we find:
Velocity = 1.57m*3.34 rad/s = 5.24 meters per second. That’s equivalent 11.7 mph.
So that’s how fast a fly sitting at the end of the Cybertruck’s wiper blade would be traveling at max wiping speed. The F-150 Lightning’s wiper blades — which appear to sweep the same angle in the same amount of time — are 22-inches long; add maybe seven inches at most to account for where the part of the wiper arm below where the bottom of the blade wipes, and it’s about half the length of the Cybertruck’s, meaning its “r” is half of the Cybertruck’s, resulting in half the blade-tip velocity — so about 6 mph.
One thing I want to address, since we have so many nerds in the audience: Is the Cybertruck really wiping 90 degrees? That Alex on Autos YouTube video appears to show much less than a 90-degree wipe. I think this is a bit of an illusion, since the wiper arm has a bend in it, and the pivot point isn’t shown (as a result, making one “assume” that the pivot point is farther to the right than it is in reality). In truth, the tip of the wiper is pretty much directly above the wiper’s pivot point when the wipe starts (when viewed head-on), and when the wipe ends, it’s pretty much directly to the left of it (on the same horizontal plane). Maybe the wiper is 85 degrees; that doesn’t change our answer much, bringing it from 11.7 MPH to 11.
So conservatively, to those of you flies planning to take a joy ride at the top of the Tesla Cybertruck’s enormous windshield wiper: Get ready to travel 11MPH. It’s possible you’ll travel even faster towards the middle of the wipe, since it takes time for the blade to accelerate and decelerate, and I just used an average angular velocity for these calculations.
Now, if the vehicle is moving forward at 30 MPH, how quickly will the fly be moving at different points in the wipe, since the vehicle’s velocity will be additive to the wiper tip’s velocity? That’s maybe an article for another time.
This article gives me horrifying flashbacks to school, but your one paragraph about the unit circle just being coordinates clarifies it so much more than any of my professors managed to.
Windshield wiper speed? Who cares? My guess is windshield wiper costs. I looked at a set of wipers for my 2007 Toyota Camry a set of of a 24 in and 20 in is $39.99 each. Now why a 4 inch larger wiper is the same price I don’t know. What I do know is Big Lots, nd Ollie’s charge less than half. Also Amazon has the same OEM Quality for about half. How much a 6 foot wiper cost is probably insane. Does any other vehave a 5 foot wiper? Tesla people need psychological help.
Then why did you read it? Also, what’s your guess about the costs?
I once had a grasshopper hang on to bare glass until about 43mph. Your hypothetical fly should have no issues in city traffic.
My 1987 Subaru XT6 also had a single wiper. If the glass wasn’t perfectly clean and the wiper blade “just out of the packaging” I would always get streaks on the entire outer half of the arc. I’m sure the same will happen here once these invasive trucks migrate northward to where there is winter and grim.
Here’s a tip. If you are thinking of a Cybertruck, wipe that idea from your mind and fly away with high velocity.
I thoroughly enjoyed this pointless yet informative article.
Brand new wiper is already squeaking 😐
This is the kind of hard hitting deep dive journalism the world desperately needs. Thank you David Tracy, you are doing humanity a service.
I find the wiper the most interesting thing about the Cybertruck, so good job! Also, could you use a radar gun on it?
Oooof! Interesting, but way too much math for my wrinkled old brain.
More wrinkles=more smarts. But yes. That is too much math for my billiard ball brain
This does seem pointless but let’s bring in Jason and get into some real science. A fly traveling at that velocity would surely have the scat scared out of it. Car nerd scat enthusiasts want to know the velocity of scat leaving a butt on the tip of the wiper. Pull in the high speed camera guys on youtube and…well, the accolades will just start rolling in, I assume.
“They appear to be rotating so slowly, but if you count — one Mississippi, two Mississippi — how long it takes for them to make one revolution, and you know the length of a wind turbine (they’re quite long), you realize that the tips of those blades are doing, like, 100 mph.”
Not sure how much each blade on a modern wind turbine weighs but the sheer mass and inertia must be quite astonishing.
In 1940-’41 Smith-Putnam, with some government support, built a ginormous two-bladed wind turbine on a hill called Grandpa’s Knob outside of Rutland, Vermont; it was some 40 years before it was eclipsed in size. https://www.ydr.com/gcdn/-mm-/9ad579d9ac198968e69213f707edff994152e1d2/c=12-0-396-512/local/-/media/2015/08/13/YorkDailyRecord/wp-PPYR-YorkTownSquare-1251-smorganX00113_9.jpeg?width=383&height=512&fit=crop&format=pjpg&auto=webp
This gives an idea of the scale (obviously pre-OSHA, ha):
https://www.arcgis.com/sharing/rest/content/items/7fc2447c836047059b73b002a613d702/info/thumbnail/ago_downloaded.jpg?w=800
The blades were between 8 and 11 feet wide and 65 to 66 feet long; each one weighed eight tons!
They do indeed look to be moving at a leisurely pace: https://youtu.be/7H8SqOAvZ5Q?si=k2bNMBq42M4bNiXW
The wind turbine operated for a couple of years, producing between 1 and 1.5 MW, making it the world’s first megawatt wind turbine. Some maintenance issues & some difficulties with repairs due to wartime conditions led to the wind turbine being idled for two or three years. Upon repairs being completed, in 1945, the wind turbine operated for about three weeks until one of the blades broke off and landed about 750 feet away. One can only imagine the immense forces involved in throwing a 8-ton blade more than two football fields or two soccer pitches.
Couldn’t you just :
Yes, but that incurs two problems; most measuring devices are not designed to measure curved lines, and you’ll leave sharpie on your windshield. The latter problem is fairly easily resolved with some alcohol and a rag, but the former will inevitably introduce inaccuracy.
“you’ll leave sharpie on your windshield. The latter problem is fairly easily resolved with some alcohol and a rag”
Yeah, but that doesn’t resolve the problem that you’re still left with a Cybertruck.
That is also easily resolved with alcohol and a rag.
This may be the greatest molotov cocktail joke ever.
That will probably stain the body and void the warranty.
This deserves Comment of the Month—if not the freaking year
“most measuring devices are not designed to measure curved lines”
Use a piece of string to follow the curve. Then measure the length of the string.
This is the type of technical content we don’t find elsewhere!
Pure gold.
62 inches?? When this idiotic thing was first shown, I joked on social media, “Coming soon to an auto parts store near you: 48-inch wiper blades.” Little did I know I’d be over a foot short!
Is Trico making these? Because I want one in my store just for the lulz.
Hopefully the wiper is just a generic parts bin one off a commercial vehicle. Buses have some pretty massive wipers.
The biggest wiper I’ve ever seen cataloged before this is 40″. We’ve sold a pair in the past, the biggest we stock is 32″.
Sitting in the back of the bus, the wipers look big, but some quick googling shows most bus/RV wipers in the 32″ range.
Crazy that this thing needs double the length wipers than vehicles with seemingly giant windshields.
Most modern semi trucks use 22 to 24 inch blades
I’m actually disappointed in Musk.
I would have expected this to be 69″ long.
Lets get really nerdy and answer your final question. You ask “how quickly”, which is another way of saying “what is the magnitude of the resultant velocity vector?” The Cybertruck’s windshield makes an angle of 18 degrees with the horizontal according to my protractor (extremely flat, most cars are 25-35 degrees). When the wiper is moving solely in the vertical direction at the very start of it’s upstroke the tip velocity will be directly opposing the forward velocity of the car, so it’s the minimum speed the fly will have, can be calculated by 30 mph – (11 mph * cos(18 deg)) = 19.53 mph. When the wiper is at the end of it’s stroke and moving directly horizontal it’s perpendicular to the vehicle’s own velocity vector (and the angle of the windshield doesn’t matter), so you can just do some vector addition and arrive at: sqrt(30mph^2 + 11mph^2)= 31.95 mph.
On the downstroke the horizontal value remains the same (opposite wiper velocity direction but keeps it’s magnitude), but the last moment before parking you get 30 mph + (11 mph * cos(18 deg)) = 40.46 mph.
would a fly be faster if it just flew on it’s own, rather than just sit on the end of the wiper?
2 m/s is the maximum speed of a house fly (honey bee (queen) can do 8 m/s)
What about an unladen swallow?
What do you mean? An African swallow or a European swallow?
I don’t know… YEAAAAA!!!!
yes
Do we need to explain this thread to David??
Nerds! Nerds everywhere!
I love it
at which point in the flight did it become unladen?
I am just barely tall enough to ride this ride!
I really wanted to enjoy this article, but sadly, I don’t speak Sinese.
Don’t worry, you can still get a loan for school as long as you have someone to cosine.
Don’t go off on a tangent
That’s getting to be a pretty big pun loan. You’ll need someone to cosine it.
Since we are being nerdy here, I’d wager that the wiper tip’s peak velocity is a tiny bit higher than what you’ve calculated. In order to complete a single sweep, there is a period where the wiper is accelerating, a period where it reaches its peak speed, and a period where is decelerates to a stop, before changing direction. Simply taking the amount of time the wiper takes to complete a sweep gives the average velocity throughout the sweep, but not the highest instantaneous velocity.
This is similar to having a car do a quarter mile drag race in 10 seconds, and therefore extrapolating that is its velocity was 90 mph (1/4 mile in 10 seconds = a mile in 40 seconds = 90 miles covered in 3600 seconds).
In reality, the peak velocity would have been much higher considering the car went from stationary to a much higher speed. I’d also be the first to admit however that the wiper likely experiences a much more brief period of acceleration and travels at a more constant speed than a car accelerating the whole way down a track, so the peak speed is probably not a whole lot higher than 11mph anyway.
I do mention this in the article!
My apologies! I missed where you mentioned this towards the end!
I will say, this article got me thinking about wiper motors more than perhaps I ever had before. Is there an aftermarket for wiper motors? People modding their setups to sweep across the windshield faster than OEM? Beefed up wiper transmission/linkages to handle the increased torque? Folks meeting up in parking lots on a Friday night to see whos wiper can dispatch a cup of water the quickest? The possibilities are endless!
If we are being truly accurate it is actually accelerating the entire time towards the radius of the arc, even when the magnitude of its velocity is constant.
Yes, David is calculating the average velocity and usually the linkages create rotational speed variation that likely has a much higher instantaneous velocity at various points in the swipe.
The answer 4 months out of the year is zero. Because that exposed wiper would be frozen solid to the windshield. No need to show my math.
You’ve got both 90 degrees and 270 degrees as pi/2 radians. I think you want 1.5pi radians for 270 degrees, or 3/2pi radians if you prefer fractions (unless we’re counting absolute radians from 0 degrees, I guess?).
As somebody who grew up doing orienteering and shooting, I can do all the minute-of-angle stuff offhand, but anytime somebody hands me a problem to solve in rads or milirads I end up with a headache.
I just remember degrees * pi/180 = radians, and do my human meat computer thinking in degrees, and do my trig in radians, converting back and forth as needed. 🙂
I just remember one radian is 57.3 degrees.
This comes in handy when we need to work out some rough geometry. When the angle is small (say 6 degrees, or 0.1 radians) the sine and tangent values are almost identical to the degree itself. A 6 degree angle will have a sine and tangent value of 0.1.
Once I was in a meeting with some lighting consultants on how to angle their spotlights such that from the roof, they point at about 30′ from the base of the building. The building was about 600′ tall so some quick mental math told me that:
Often quick and dirty does the job.
Yep, I often use that same trick when calculating angles from road grades (grade = rise/run in %). Up to 10% grade the error from assuming grade == radians is less than 1%.
So….. if the truck was doing 50mph down the road, and a fly was sitting on the end of a moving wiper how fast would it go? lol
If a fly started in one city on the tip of a CT’s wiper, and another fly started in another city 50 miles away on the tip of an F150’s wiper, which fly would be blown off first and smashed on the windshield of a semi?
According to SNL-LOL’s School of Shadetree Engineering:
Short answer: a hair over 50MPH–say 51?
Long answer: square roof of (50×50 + 11.7×11.7) = 51.3
Reason: if one component is several times larger than the other, perpendicular one, the resultant is pretty darn close to the larger component
Source: 24 years of running numbers in the field, often in my head, just to get a ballpark answer to see if something makes sense
“Velocity = 1.57m*3.34 rad/s = 5.24 meters per second. That’s equivalent 11.7 mph.”
There is no direction component here. This is not velocity.
/being a bit salty after his son got tricked in the physics quiz. I’ve been telling him since the beginning of time that if a question looks easy, it never is.
Isn’t the direction “along the arc of the wiper tip?”
I think it would actually be tangent to the arc of the wiper, at the tip.
Indeed, it is tangential velocity.
It’s true, technically it’s v = omega CROSS r.
But we care about absolute value here.
I like the nerdiness, though!
We structural engineers are probably the LEAST anal about these things. We usually need not worry too much about conventions and accuracy. No one gives two shits if my answer is off by a percent or two.
fs of 2.5 takes care of all of that.
FS of 2.5 makes me do extra math, FS 10 and (usually) we can just do a SWAG/ high-level check and call it done.