The Real Physics of Roller Coaster Loops

A look at the physics principles and calculations that engineers use to design roller coaster loops.

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Video Attributions:
“Wildfire Front Seat POV - Silver Dollar City” by AmusementInsider
“(4K) Kraken Back Seat POV - SeaWorld Orlando” by AmusementInsider
“Holiwood Nights 2017 | Voyage and Thunderbird Behind-The-Scenes Tour! Holiday World” by OhioValleyCoasters
“Dragon Challenge Off-Ride POV | Universal Orlando Islands Of Adventure 20” by OhioValleyCoasters
“Batman The Ride Off Ride Cinematic Footage [Six Flags Over Georgia 2019]” by OhioValleyCoasters
“The Incredible Hulk Roller Coaster! AWESOME B&M at Universal Orlando! Off-Ride POV HD” by OhioValleyCoasters
“OzIris - Parc Astérix (4K 60FPS On-Ride POV NO COPYRIGHT)” by Coaster Hipster
“The Monster - Walygator (4K 60FPS On-Ride POV NO COPYRIGHT)” by Coaster Hipster
“First Person Riding Roller Coaster "Medusa" at Six Flags” by Brian Wilson

Still Image Attributions:
“Raptor at Cedar Point in motion” by Craig Lloyd
“Centrifugal Railway Detailed Sketch” by Unknown author
“Revolution” by Prayitno
“ASTM F24 Logo” by ASTM International
“Carolina Cyclone (Double Loop)” by Coasterman1234
“Euler spiral” by AdiJapan
“Europa-Park - Blue Fire Megacoaster” by Jérémy-Günther-Heinz Jähnick

Music from Epidemic Sound

#RollerCoasters #Themeparks #ArtofEngineering

[AVdE]

When I clicked the video I thought this was just gonna be a brief explanation on why circular loops can cause whiplashes, and thus they use more egg-shaped designs. But mad respect for the incredibly detailed and in-depth explanation given!

[Smashbro]

I like how so many early engineering designs and inventions were basically just death traps

[dylandowling]

A real world application of calculus?! I never thought I'd see the day...

[ArtofEngineering]

Quick note! If you are going through the math in this video yourself, please note that the derivation at 13:03 contains an error. The first equation for "G" has the "g" term in the wrong place, and the correct equation for "G" is shown at 3:50. The resulting equation for "r" should have g*[G - cos(theta)] as the denominator. I hope this helps if you're trying to replicate the plots and it doesn't work properly.

[AmusementInsiders]

Always love how informative your videos are! Keep up the amazing work man!

[trueamerica]

Thats why Tony Hawks first Skateboard Looping attempt was a total failure...he build a circular loop, which caused the high changes in g forces making it also extremly dofficult to ride.

[AlexAn]

No kidding, the most interesting video I've ever watched. I hope that you ll make more videos in the future that shows the practical use of mathematics. Keep doing!!!

[fintamin]

Finally an excellent video to showcase this matter! Not only does it explain the maths, but it also dives into other aspects of a loop as well. Very very good job. /engineer

[brennaobrien]

I’m taking algebra 2 right now in high school and have wanted to be a roller coaster engineer since I could remember. I love this explanation. I can’t *comprehend* it, but I kind of understand it. This makes me want to engineer roller coasters even more. Mathematics is a fascinating subject.

[nicholasr]

We'll need to use a little calculus.


* *busts out Diff Eq*

[clcoolgaming]

This guy really deserves to be appreciated the level of depth in his technical analysis is just amazing! Keep the up the good work man!

[psu]

Love these videos! As an engineering student, it helps me put together all the components I learn!! Thanks!

[bleeve]

This is why us unprofessional coaster designers use FVD and NoLimits2. It spares us from this headache of math.

[NguyenHaNhutLong]

Thank you very much for giving us an insight into these mathematical derivations. It gives me a better insight into how engineers work out a design of a specific task. I hope you will keep up doing more good contents like this!

[rcmaniac]

Holy Math, Batman! That was an amazing video. As a software developer and coaster/theme park enthusiast, I've often gone "I want to play Roller Coaster Tycoon, Parkitect, Planet Coaster, No Limits, etc." but once I hit the limitation of them, gone "what is needed to make my own version of these games?" but get stuck at the math. I don't have the time to make such games, and don't know how they came up with their calculations or similar, but to see the math that is needed just to do a loop is awesome. It makes me want to try and make my own game (again... no time...), but it's so interesting to see. Also interesting to think about how early designs such as Arrow and Schwarzkopf were done before computers really had the computational capabilities to make such designs, and to think how many limitations of the formula come from "the train doesn't have enough flex to be able to do that tight of a loop" and still needing it to fit within safety calculations.

[spb]

Neat. I’m in calculus right now and watched this when it first came out but didn’t understand it then. I still wished you did more math to explain what was happening when you were doing partial derivatives

[vinimetal]

Holy shocks, you need an engineer degree to understand this video for real

[OkOk-tugc]

I learn more in these videos than I have ever learned in school science class. I sometimes wonder whether that is good or bad.

[spencebot]

I don't know how I hadn't seen your videos before, they fit perfectly with my viewing history. This is my favorite kind of video, basic math and engineering to explain things I hadn't really thought about. Please keep making awesome and informative videos.

[TimMc]

Amazing video! Maybe do one about the physics behind zero-G/heartline rolls?