The Rocket Equation: Mathematician vs Astronaut
ฝัง
- เผยแพร่เมื่อ 3 ก.ย. 2020
- Huge thanks to Chris Hadfield and their amazing team for making these videos possible. chrishadfield.ca/
You can watch just my rocket equation derivation without the coolest person in the world getting in the way. • The Rocket Equation: a...
You can go and watch Lucie Green's first two video with Chris Hadfield right now, the third one with 'aurora surfing' is out in a week.
• How the Space Shuttle ...
• The Story of Space Shu...
Here is my previous video with Chris where we talk about Orbital Mechanics.
• Orbital Maths at NASA ...
Our trip to NASA was organised by the fantastic folks over at Cosmic Shambles.
cosmicshambles.com
/ cosmicshambles
With thanks to NASA and the team at the Kennedy Space Center Visitor Complex via agreement with Trunkman Productions Ltd and The Cosmic Shambles Network. To discover more about the KSC please visit www.kennedyspacecenter.com/
Free resources for teachers!
We have a complete guide to the mathematics in this video as well as some student worksheets and activities.
think-maths.co.uk/standupmath...
CORRECTIONS
- One fantastic correction from Dogan Erbahar which I will paste a copy of here:
"When equating the momenta you already put the minus sign in front of v_e. But then at the end you are again substituting on the equation. The resulting equation is correct but that minus sign is there not because of v_e. It is there because your dm is negative that your rocket is losing mass. So should be placed in derivation."
- Let me know if you spot any other mistakes!
Thanks to my Patreons whose generous funding I used for a vacation to Cocoa Beech Florida NO REFUNDS.
(Or maybe everyone involved donated their time, covered their own expenses and my Patreons only had to pay for that flip-chart. True story: I bought that flip-chart in the USA as it seemed silly to fly one over from the UK and afterwards the NASA outreach team kept it, which I think means it officially 'works at NASA'. That flip-chart now has a cooler job than me.)
Here is a random subset of those fine Patreon People:
Baadrix
Stephen Tierney
Erin Eldridge
Christian Gruber
David Wagner
Richard Fourie
Nicholas Koceja
Kristian Joensen
Andy B
Jordan Scales
Filming and editing by Trunkman Productions
Extra help during the shoot thanks to Melinda Burton and Joanna Gostling
Flipchart by Matt Parker
Audio by Peter Doggart
Music by Howard Carter
Design by Simon Wright and Adam Robinson
MATT PARKER: Stand-up Mathematician
standupmaths.com/ - บันเทิง
Engineers: let’s add 30% for rounding error.
Factor of safety my dude :D
That's me playing Kerbal Space Program, spending 2 hours planning a mission on paper and then having it explode in 2 minutes.
thats like the maximum overloading condition
Oslier that’s me calculating delta v in KSP.
e=pi
"8000/3500 ... that's about 2" "and e is 2.7 ish"
As a physics student, the amount of rounding going on in this video was just perfect
and in the next sentence e was rounded to 3. now it is truly perfect
In my astrophysics class, the professor was an absolute expert at this kind of rounding. Pi on top, 4 on the bottom, enh, just cancel them both. Ooh, this integral is hard, but this sin term won't change much across our limits of integration, so enh, just call it a constant and pull it out of the integral and now it's just a polynomial.
Once he derived Chandrasekhar's limit from the basic physics laws, and in about half an hour of showing us all the leaps of thought, wound up with a numeric value that was surprisingly close to the actual value, within 25% or so.
He'd always finish out these derivations by comparing what he got to the accepted value, and then say "Enh, that's close enough for government work."
[Edit: 25% is probably an exaggeration, he was probably further off than that. Another of his favorite quips was "after all those approximations, shortcuts, and simplifications, if I can get within a factor of 2 of the right value, that's pretty much bang-on as far as I'm concerned."]
@@cvkline Absolute CHAD teacher you got
Charley Kline astro guys are always pros at this. π? 1 is close enough lol
@@cvkline For one Astronomy class in first year, we had to memorise 20 equations and be able to derive 10 of them. The derivation for tidal forces we got shown went over several pages and used multiple subtle approximations.
The recommended textbook for that year's astronomy just differentiated the equation for gravitational force, and then swung the dr to the other side. 3 lines.
Me trying to sleep...
My brain at 3am: inaudible maths noise while Chris talks about rocketry
Me, trying to concentrate on both audio channels at once:
😊 ☺ 😐 😳 😵 🤯 🤕
Don’t forget the music too
Finally, I've seen a "e is more or less 3" in the wild!
So e “is more or less” Pi
It's the Parker "e".
E = π
Oh, you haven't seen anything. There are certain calculations in cosmology in which physicists round e = 10.
@@angelmendez-rivera351 madness
"Let's say 8..."
"8 is an easy number"
"...thousand"
haha
Still an easy number. The “...thousand” part is just an order of magnitude issue.
Peter Knutsen spoken like a physicist
It's a very rough estimate. I can't remember where the difference starts to be meaningful, but that's the wrong equation for gravitational potential energy above a certain height.
@@Mad_Elf_0 It depends how far up you are compared to the radius of the Earth. If you are 400km up, and the radius is 6371km, then the approximation is still reasonably good. But if you try to go to the Moon (384 400 km) then that "mgh" bit is completely wrong.
"and you're just a bit of metal and flesh…"
Chris Hadfield, bionic man
Gladly, they didn't have to rebuild him for six million dollars.
I like how "Oiled Cement" is the best analogy he could come up with for near frictionless space flight
@John Smith thats what i said
@John Smith yea
Yeah i kinda raised an eyebrow at that. Haha.
Sounds like he's trying to convey that it's still got some vibration to it, but a surprisingly small amount
@@Norsilca Possibly so! However, untextured concrete actually has a very low friction coefficient. It gets textured in order to combat this, mostly using float or broom finishes. I'd say that this probably wasn't what he had in mind making the comment, but it works even better than at first glance!
"That's actually what astronauts fly on.
- Maths."
Should be a t-shirt.
"From the wheel to the skyscraper, everything we are and everything we have comes from a single attribute of man - the function of his reasoning mind."
@@thanasispapadopoulos7922 in France "maths" is most commonly used, for "mathématiques" (plural). Though some people use "mathématique" (singular), like Cédric Villani, who is known for loving old fashioned behaviour and style.
The plural seems right to me, at least until the unification is complete ! :)
en.wikipedia.org/wiki/Langlands_program
ok nerd
Maybe the US edition could say math, but maths is not incorrect either.
"That's actually what astronauts fly on. -Meth." Would sell better though!
For anyone who is interested... given it cost approx $54,500 per kilo for the space shuttle (once you add in the R&D, vehicle & program costs etc.), that's $54.50 per gram.
The mass of a righteous moustache like that sported by Chris is approx a third of a gram, thus, it cost NASA about $18.17 to fire that bristly lip warmer into the void each trip 👍
That's why astronauts are required to go to the bathroom just before launch
I had a late night and an early morning and I was watching this on the bed after work so I dozed off for a moment and then I opened my eyes and saw Chris looking directly at the camera saying "you're lying on your back." and I had a bit of a panic moment.
PoV: Chris Hadfield has kidnapped you and strapped you on to a rocket.
That was hilarious, thank you for sharing
How was the launching?
Chris is one of the nicest guys. So approachable and friendly. I pleasure to work with when I did work with him a decade or more ago!
What work you did with him
I'm deaf in one ear. I had to watch this twice and wear my headphones the wrong way round. It was worth it.
rip man
Sorry to hear that. Matt has a video with just maths audio in the description if you need it. :D
me too
Yeah
respect
Sad fact: that 10-15% of "payload" is actually about 90% structural components of the stages. Only about 1-2% of the total initial mass is the real final payload.
I was wondering about that, too.
@Jason Bowman Well it was before spaceX got so cheap. Now is somewhere along the lines of $2.5k per kg.
@Jason Bowman The price has gotten slightly lower.
If the weight of the Shuttle itself is counted then about 5% or the starting weight reached orbit. Those 450s isp engines are awesome.
@@zapfanzapfan Those 450 isp engines are actually pretty stupid as they cannot lift the vehicle by themselves. So you always need those massive SolidMoneyBurners To get you up there.
"Your F is steady and your m is going down... your a is going up"
It really is
Came here to post this. That's some truth right there.
*Approximately
lmao
3:25
I love how Chris takes the battle by pushing the camera too far from the whiteboard, making it impossible to read 😂
Matt: "I am an SI unit kind of individual."
Chris: "Yes, you are."
Most people are.
I want to be patriotic but I just can’t lol, SI is better in every way
What's an SI? Sorry I'm a caveman trying to catch up
@@deograciascorderoii7299 Système international (d'unités), i.e. International System of Units. It's a common standard of measurement units used in all of sciences and most of the world - metric system. Most notably not used in USA.
And here I was thinking I’d never understand poetry, thank you Chris.
And Matt I guess…
Poetry with explosions is the best kind of poetry.
Nobody:
Matt Parker: e^-(8/3.5)≈e^-2≈1/9
I wonder why they say he does math like a physicist
I was hoping he'd approximate it as e^-e
It's a parker e.
@@SimonBuchanNz hahahahahah! I was waiting for that one! :P
TBH it is pretty close considering those roundings. XD
e^-(8/3,5) = 0,1017013923042268292630681245966135276786674905359158653442327045...
1/9 = 0,1111111111111111111111111111111111111111111111111111111111111111...
Matt: Thats an order of magnitude, lets ignore it.
Astronauts: Not so fast dude!
All of the KSP players are thinking, "Well, if you're going to bother with gravitational drag, you need to factor in atmospheric drag as well."
Before or after the first few rapid unintentional disassembly events?
@@technicalfool During usually. One of those, "Oh, yeah. That's why I'm not going to space today," moments.
Ah yes the KSP Kracken... Lost many a beautiful rocket to its sometimes janky physics engine... But love the game anyway.
What the hell is *Gravitational Drag*?
That moment when you realise you have totally underestimated how much extra dV you should allow for the atmospheric drag on your latest creatively designed monstrosity...
Mathematicians idea of fun: drawing arrows in RED!
Yes Comrade
Sometimes we spice it up and use orange!
Ok one technical detail. When equating the momenta you already put the minus sign in front of v_e. But then at the end you are again substituting on the equation. The resulting equation is correct but That minus sign is there not because of v_e. It is there because your dm is negative that your rocket is losing mass. So should be placed in derivation. That's how books derive it. (Confuses me also everytime I try to derive in class...) very good video, thank you anyway...
Well spotted! I’m always loosing track of my negatives (and tend to just make sure I’ve made an even number of mistakes). I’ll add that to the corrections.
Negative infinitecimals? You just broke my brain.
To put in other words, "I don't know how but you used the wrong formula but got the right answer"
P.s: Please don't attack me, i know it's not true!
@@standupmaths don't worry. worst case: the rocket decelerates and the astronauts burn up in the atmosphere
Yeah just do it in rocket frame much cleaner.
"When your 'F' is steady and your 'M' is going down, your 'A' is going up." -- Chris Hadfield tells an astronaut dad joke.
You can mock me all you want but I don't get it...
Chris Kacso F=ma. If F is held at a constant value, if m gets smaller then a has to get bigger and conversely.
And how is that a joke?
@@user-un7gp4bl2l I am familiar with the preachings of the Lord Sir Isaac Newton and the 2nd law of motion, but I don't get why is it a [dad] joke
"Your A is going up." Your "A" is what you're sitting on...
What a bad time for my headphones to be broken. :(
Edit: ok if I turn on mono audio I can hear Chris clearly and Matt has a video of just the maths available on his second channel! Crisis averted!
just turn them around
*chris-is
FTFY
"The greatest compromise ever made for a spacecraft." Damning with faint praise if anyone ever did.
You missed the most important thing that makes aeroplanes more efficient: They don't have to carry their own oxygen XD
Yeah and they get to push off the air behind them. Jet engines get Isp of like 25000 m/s.
@@appa609 they don't exactly push on the air behind them. They use the air as reaction mass so they can go for the best ratio of flow and thermal expansion for thrust. Simply not carrying oxygen would only double the efficiency but in reality it's like 10x more efficient
Mason Daub We're saying the same thing.
@@appa609 No you're not! No "pushing" on the air involved.
@@appa609 Jets and rockets are *more* efficient at lower external air-pressures. Having air behind the jet does not help in any way whatsoever - it prevents the exhaust from escaping.
They do not push off anything. That's a silly idea which silly conspiracy theorists claim, when saying rockets can't fly in a vacuum.
It's simple. You squirt gas in one direction, and you go in the other.
Like, if you fire a gun, you go backwards. It doesn't matter whether the bullet hits anything or not.
Imagine visiting and seeing Matt Parker and Chris Hadfield just hanging around. What a treat that would be.
17:26 that's the face a mathematician would do when hears the word 'combination'. A pure expression of joy.
"As the engines start to bend and warp your vehicle."
Sounds like what happens in Kerbal Space Program.
Happens in real life, too! Rockets can be bendy!
@@MattSimmonsSysAdmin Not just "can be", they really are bendy.
*M O A R S T R U T S*
RUD... 😩
I watched the maths! “I’ve been told integrate like a physicist!”
Pure Chaos; Chris to camera, the alarm, and Matt muttering in the background. Love it!
You did a good job editing this together, it looks like this all took lots of effort. Great video! Enjoyed it very much!
I derived this equation only once in an online propulsion class. But now I realized it was just a velocity differential that I was calculating. I'm subscribing this channel right away.
Finally someone got around to deriving my equations. Good job, comrades!
Very interesting but overtly simplified. as Chris said around 15:00. In this example we only considered a single-stage rocket without parts of considerable mass being jettisoned (SRBs,pwyload fairing, launch abort system, subsequent stages). Works for stratospheric (sub-orbital) rockets, but anything like Saturn or SLS is a lot more complex to calculate.
Real damn cool setting, and seeing Chris "Major Tom to Ground Control" Hadfield is a joy for ever.
This is a brilliant episode! And perfect timing, because space programs around the world are accelerating us into the future of space travel!! Thanks for this wonderful episode!
Chris Hadfield is so cool. Just look at all that swagger oozing out of him here
Chris Hadfield the greatest Canadian Astronaut ever.
I applaud you for keeping your composure vs Chris Hadfield. Omg.
Thanks Chris for space oddity!
Matt called it Cape Canaveral and not Orlando. I’m so proud of him!
Closer. But, KSC is on Merritt Island. :-)
Oh man I'd LOVE to hang out chatting rocket physics with Chris. He's a proper legend.
Chris is such a BA. Huge fan. Started talking about Bob and Doug, I was like 'I watched that!' definitely one of my heroes. Great video!
Jokes on you. Only one of my headphones work, so I'm left with the maths explanation watching in confusion and wondering what Chris might possibly say in the foreground 🤷🏻♀️
Try switching your audio to mono in the accessibility settings on your phone :)
@@andymcl92 or turn your headphones around.
@@LoganStargazer that's a very nice joke
Mass of fuel is mf... **cries in Engineer**
Awesome video! I would listen to Chris all day long.
Really neat. Nice of Chris Hatfield to have played along
the last 10 seconds gave me the chill. well done.
I don't want to take anything away from the shuttle's success, but having been born in 61, the highlight of my visit to the cape, was seeing the Saturn V up close. I was awe struck. It was the reason I got an engineering degree. Enjoyed the video!
When they split the audio on the two channels, that was awesome.
Hey Matt, consider changing the thumbnail for this one! I'm sure someone else was confused like me and thought you'd re-uploaded last week's video.
Loving Chris on the show 🎉
"The very first human-capable rocket that Al Shepard flew on" Am I missing something? Al Shepard was the first American in space, but the Soviets+Yuri Gagarin beat them to the punch.
Was the rocket ready first, even though it was used second?
19:27 this has to be the best match ever
Do you see that flicker in the clouds too?
Sad I can't listen to either of these :(
Well - turns out there is barely any 'left' anyway... so I get to listen to Chris.
My plug in speakers seem to be missing Matt's part of the channel...
@@gordonrichardson2972 his part is much quieter so that you can focus on Chris if you don't have headphones, and you can hear just Matt if you watch the other video
Such a great video. Both Chris and Matt were a delight. 10/10.
I love Chris Hadfield. Dude is literally a genius on anything he wants to do.
2 astronauts casually fly in a plane overhead. "oh look there goes bob"
I spent 2 days there in October last year. Amazing facility.
I really approve of this collaboration by two of my favourite kinds of people, a thinker and a doer.
Ty for the video. Interesting how the two of you illustrated and rationalized mathematizing of rocket phenomena.
11111
hey flammy!
Pappa flammy??????
31?
Hii
876?
The video I never thought I needed.
Thank you so so so much for making this video. Loved it
Only 6 mins in and its 3am but gotta say: Great teamwork, making the Math fun and relevant, and Chris Hadfield is a Hero and a Legend, doesn't just do an awesome job, but brings it to the Public and makes it real.. If he's up for it, I want him to get to land on the Moon on a SpaceX Starship, someday.
This video brought back the memories of the Kennedy Space Centre we visited in January. It was extremely impressive to see everything these.
Hope you enjoyed it as well, Matt.
Absolutely love the audio edit of Matt fading out as Chris walks up to the camera :)
You should do two more versions of this video:
-one showing Matt as writing up the equation with the voice of Captain Hadfield as telling the details of a rocket ride
-one showing Cpt. Hadfield gesturing and we should hear Matt talking delta m and V and e and ln.
I love how he corrects himself and says “that’s how astronauts fly”. What a great dude
I was watching this with the built-in mono speakers on a computer monitor and saw that the comments were all talking about the stereo separation, so I went to hook up some speakers. I'm going to watch this again with some earbuds to get the whole immersive effect.
I love the estimating tricks. "2 and a bit, and e is 2.7ish, ... in the worst case approximation it's 3 to the power of 2, so 9". This idea of being able to go from actual to somewhat estimated to very rough estimation is a really great "number sense" skill.
Awesome awesome awesome! It’s so cool that they now have the booster rockets outside standing upright and the orbiter inside. It’s been 14 years since I last went to Cape Canaveral but I should go again and behold that beautiful orbiter.
Chris is an inspiring guy to listen to. But I would like to also recommend his son Evan's TH-cam project Rare Earth. Very interesting mini documentaries from around the world.
Great work here! Thank you for these.
One of the biggest reasons, in terms of the rocket equation, that jets are so much more efficient than rockets is that they're air breathing. Pulling oxidizer from the air instead of having to carry and accelerate it's own oxidizer.
But yea not having to fight gravity without the benefit of lift obviously plays a role as well!
9:58 Bit of a technical point here (I thought that's where you were getting at) - exhaust speed will vary depending on altitude, because of atmospheric pressure :-) equilibrium basically would be chamber pressure - outside pressure, so the higher the outside pressure, the lower the differential, and the lower the exhaust speed :-) that's why your specific impulse is so much worse at sea level! There's also intricate details about engine bell design to prevent it from blowing itself up when used at lower altitudes (if it's a vacuum-optimized nozzle it'll be bigger and subject to these issues). Great video in any case, love it!
3:31 you got that half right, I AM lying on my back, just not in a rocket ship
At 19:21 when the Shuttle engines clutch at full power and the beat drops it's a reminder to me why I love space and engineering.
Imagine sitting on top of 10 trucks of explosives ready to go off. That's frightening.
Now imagine two concurrent explainations of a rocket takeoff in different channels without headphones. Nightmare-inducing!
Well now I am sad. I have to wait until I can grab a headset to watch this, twice.
This is an awesome way to get views on vids hahaha
You can watch the math part in Matt's second channel link in description
It is nice how oversimplified this is, but still shows the essence of the problem very much.
Compilation duo is here!
I was expecting a lot more talk about rocket stages, air drag, Earth's rotation, etc. This is a nice intro.
Exceptional presentation
Cmdr Chris is such a good sport, in the 1% of the 1% of human experience. When he talks, you'd always do well to listen
That 10 to 15% also includes the rocked, at least the last stage. Lots of propellant.
I love when you guys seperate to explain seperate things 😂 so creative and hilarious
Interesting how during the derivation of the Tsiolkovsky equation, and during the discussion of multistage rockets, Tsiolkovsky is not even mentioned.
I can't even imagine what it must feel like to tap into such awesome power, to experience the sheer, giddy, visceral thrill of being able to integrate like that.
Thats a well rehearsed anecdote if ever i heard one ^^ awsome story.
This was SO cool...I tried to listen to both!! But my brain couldn't do it!!! Bravo gentlemen...you both are amazing...thank you for this. :-D
OK can we all admit we listened to hadfield first and then rewatched to listen to Matt?? dont deny itttttttt
You can switch channels on Desktop by going into DevTools on Chrome or Edge and then pasting the code found here in the console. Then hit Enter. Always hit Enter. Then type left(); (then Enter) or right(); (then Enter) to select a channel. stereo(); selects regular stereo. mono(); makes both channels the same. wide(number); will make it towards mono for 0 1. gain(l2l, l2r, r2l, r2r); will mix the channels any way you like. You could swap them with gain(0, 1, 1, ); for instance.
a few seconds in, and he talks about the "first human capable rocket" and points to an american rocket.
Yes, the US won the race to landing a man on the Moon but lost pretty much every other race. USSR: first satellite, first living thing, first man in space & orbit at the same time, first anything to the Moon, first interplanetary probe. In the late 1950s America was panicked, the USSR was demonstrating they could put a nuclear warhead anywhere in the US and the US had NO response.
Up until just a few months ago America was completely dependent on Russia to put American astronauts up. For nine years Russia had the only human launch vehicles that America could access. China would have summarily given them the finger even if NASA came begging.
I will grant that the US has won probably the most important modern race that of reusable orbital rockets. Everyone else must build reusable rockets or be left permanently in the dust.
Matt goes full engineer in this one. I love it!
I don't have a clue with any of the maths bits but its still super entertaining.
When he says he will do his maths in the left channel and Chris will talk about his experience in the right channel and I remove my right headphones
Even with right balance at 0, left at 100, master volume at 100, and youtube at 100, Matt is only the same volume as Chris. finally, with the right headphone off as well, I can hear Matt.
Or you can just use the link in the description to hear matt...
listening to Chris lets you understand what it's like to be Chris Hadfield. listening to Matt might let you experience being Chris Hadfield
Chris Hadfield is one of the best human beings known to me.
First video that I ever watched that I wish I could give two thumbs up.
I Love Mat, but when I saw Chris... I never clicked a video so fast, he‘s my hero
Another NASA+Maths video, fantastic!
That sudden long shot at 2:30 makes me wonder if they had to film this multiple times, or if they filmed everything at a distance and just created the medium shots and close-ups during editing.