In case it is helpful, here are all the Flight Mechanics videos in a single playlist th-cam.com/play/PLxdnSsBqCrrEx3A6W94sQGClk6Q4YCg-h.html. You can support this channel via Patreon at www.patreon.com/christopherwlum. Please let me know what you think in the comments. Thanks for watching!
Some smartass remark: The acceleration of the earth rotation vector can be assumed for your calculations to be the null vector, but actually it isen't exactly the null vector. Earth rotation is very slowly slowing down.
AA516: I appreciate how you touched on examples of different situations of rotating frames and how the velocity and accelerations are effected. This helped me see patterns on how the projectile motion in effected by rotation.
Absolutely wonderful. Here (finally), we find a TH-cam video lecture, which provides a balanced, qualitatively, and quantitatively accurate description and interpretation of the Coriolis and centrifugal acceleration components associated with rotating frames of reference. The examples are perfect.
Hi Michael, Thanks for the kind words, I'm glad you enjoyed the video. If you find these videos helpful, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum. Given your interest in this topic, I'd love to have you a as a Patron as I'm able to talk/interact personally with all Patrons. Thanks for watching! -Chris
AA 516: Great intuitive explanation of how the Coriolis and centrifugal acceleration terms come into play for a rotating frame. That's also a nice Bainbridge Parks Department "sun" you've got-I grew up on Bainbridge and even worked for the parks department as a summer camp counselor in high school (but never got my own beach ball...).
AE512: I like the artillery shell example. Very easy to grasp and illustrates the concept well. It's amazing how large the magnitude of the effects can grow as distances increase.
AA516: Great Lecture video Professor. All the examples with values shown are very helpful with wrapping my head around the motions seen from a body frame. I liked ALL the star wars references.
AE512: I remember being very confused with this equation in my undergrad dynamics course, but now I feel like I actually understand it. Thanks for all the example cases
Great video! The example cases are extremely helpful in illustrating the concept and dissecting how each of the components in the equation affect the true acceleration.
AE512: Quite the expression for acceleration. Hard to believe there are that many terms. But at least they can all be identified and explicitly defined as something relateble!
AA516: I was having a bit of trouble understanding how the accelerations worked out in the previous video with the playground carousel but looking at the vector math cleared alot of it up for me!
AE512: Hey Dr. Lum, thank you so much for making this: Heads up, I noticed a tiny typo on the whiteboard at 1:35:25 Where you write a_P/r = a_P/r + [Other terms] when its supposed to be a_P/b. You correct it in your next derivation step, but I definitely had to do a double take! Otherwise, fantastic video!
[AE 512] 1:01:38 The visualization of the acceleration vector helped how the ball is affected by Coriolis. Usually I am a visual person but the mathematical/vector visualization actually helped me more. Since you have acceleration, you could solve for the "force" using the projectile mass?
I'm glad it was helpful. There are several related videos on the channel. Please feel free to check them out and I would love to hear what you think in the comments. Thanks for watching!
AE512: @27:10 you talk about how the angular acceleration relative to r is equal to the angular acceleration relative to b. However, in the Coriolis derivation video I thought we defined that only to be true when we choose r_p/b to be equal to w_b/r... Perhaps you'll elaborate on this later in the video...
AA 516: Again, the perfect way to understand these concepts is in this video! Just a small typo at 1:31:56 I guess that made me a little bit confused there 😜 a_{P/r} = a_{P/r} + 2(...) +...
AA 516: Hi Professor, this is a great video and very easy to follow! I do have a question though. I'm not sure if you have already answered this but for Case 2, shouldn't the a_p/r = [0 0 -9.81] and not the a_p/b term?
Thank you very much for such an amazing video. But one thing is hard for me to understand at 1:00:18, and that is a_p/r =[0 0 -g]'. What I understood is that, a_p/r is the acceleration of vector p w.r.t to the reference frame. How are the first 2 terms zero? Because from the reference frame, observe can see that position has non zero acceleration in all 3 reference frame axis.
You said we live on a rotating sphere. Do you have a physical measurement of earth curve or earth radius? Also, why don't we observe an apparent deflection (Coriolis effect) of objects in the air as we observe them from the ground if earth is a non inertial spinning reference frame?
AA516: Professor, it's a great video as usual. So, the accelerometer measures using Earth as a reference frame and the plane as a body frame, is that right? (Name: Daniel Teshome)
AA516: Is it safe to say that the fictitious Coriolis Force and Centrifugal Force are sort of like torque in that they are zero when projectiles are moving along the axis of revolution?
Shouldn’t the centrifugal acceleration at 1:06:20 be [-1.64 0 0]^T? Omega cross r in parentheses has a direction of y and omega cross y has a direction of -x Edit: you just forgot the minus sign before the equation there, we are observing the motion from the frame b.
The only thing hard to believe about this video is that a cadet fresh out of the Imperial Naval Academy would be given such a prestigious assignment on a Star Destroyer. You have to prove yourself in the most disciplined Navy in a galaxy far, far away before making that kind of career leap.
Hi, Great stuff. at time 39.40, you said centrifugal acceleration. I think this term is commonly refered as centripetal acceleration. Centrigugal is an inertial force with a minus on the centripetal acceleration?
AA516: At 1:07:38 , you say that as Edward steps off, the same effects are seen. The tangential velocity of his throw is not folded into the V vector. So when he is sitting on the ground, he throws it at some velocity v + v_tangent to make it the same throw? In this case, the ball has no idea that is has been thrown from the ground, because its velocity is the same as the throw from the edge. So the V vectors are the same, and you described how the P vector is just slightly different but not meaningfully. So the last question is - is our omega the same? I think it is because we are in frame b so regardless of where p is or what v is, we are still going to have the angular acceleration from our POV (not edwards, though).
I am also tripped up by leaving Edward behind as we rotate if he steps off. But I think it is just an intuition thing because we also leave behind the balls as we throw them (whole essence of this is how to quantify this leaving behind?) since our hands no longer apply the force to keep them spinning with b.
Hi MIles, ah I see your question, thanks for the timestamp. Basically, what I'm saying is that it doesn't matter if Edward is on or off the merry go round when he throws the ball. Both cause the ball to fly in a straight line from an inertial perspective. However for Brian who is rotating, he doesn't care if Edward was on or off the merry go round when Edward threw the ball, both cases produce the same motion from Brian's perspective.
AE512 ibraha5 Very interesting lecture. I have a question, since things weigh slightly less at the equator does that mean they consume less fuel for example Rockets and aircraft? Thanks
At 34:39, calling it "translational" seems incorrect, there can be rotation too. Some people simply call it "the acceleration of the origin of the moving frame" (relative to the frame of reference). But you are not the only one who use that term, is it through misuse of language ?
Great lectures! I have a question which can be applied to this and previous video: For example at time 27:14, about the angular velocity vector/derivative , you write w_b/r = w_r/b is it mean that vector components of w_b/r equals to vector components of w_r/b and there no need to rotate ang. vel. vector between the different frames? or maybe it means that the ang. vel. vector is the same for each frame but has different coordinates? Best Regards Thank you for your material!
Hi Oleg, Thanks for reaching out, I'm glad you enjoyed the video. Unfortunately I'm unable to respond to questions on TH-cam due to the sheer volume of inquiries that I receive. That being said, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum as I'll be able to answer questions there. Given your interest in the topic, I'd love to have you as a Patron as I'm able to talk/interact personally with Patrons. Thanks for watching! -Chris
In Case 2 (minute 1:06:15) we find the acceleration terms with respect to the body frame, but what if we wanted to find them with respect to the inertial frame? We know from the intertial frame's perspective we would see the ball going down (without any deflection), but what would cause all those coriolis, centripetal, tangential, etc terms to become 0?
So in reference to u other videos with drone.... Which reference are we describing the P. And what does the Position vector of p in reference to R represent ( in terms of drone video
AA516 - Fantastic lecture! Just one question: at 1:50:50, why does the velocity vector of the artillery shell become V_P/r, instead of V_P/b like earlier?
Gary, excellent catch, that is a typo. I've added some notes in the description of this video to highlight this correction/errata. Thanks for keeping such a sharp eye out! Please let me know if you find anything else fishy in any other videos, thanks.
AA 516 I am wondering the effect of the fact that these projectiles are moving through a fluid (the atmosphere) which is also rotating at roughly the same rate as the earth body frame. Does this fact cause a damping effect on the predicted magnitudes of these coriolis accelerations?
Hi Joseph, you bring up a good point. The atmosphere is also subject to these forces (think about the hw problem about cyclones and hurricanes). That being said, the aircraft will experience local aero forces/moments due to moving through this fluid. It is just a matter of resolving the directions/magnitudes of these effects. We'll explore this during our discussion on wind tunnel testing.
Dr. Christopher, I had a doubt. First of all, Thank you for the amazing video series. My doubt was that at 2:11:32, you say that the accelerometer measures "True acceleration". So if that were true then the accelerometer placed stationary on the ground would measure "Omega^2*r" but the actual accelerometer reading is not "Omega^2*r ~ 0.0338 at the equator". I am confused. I read it on Wikipedia and it says that an accelerometer measures proper acceleration (Normal Reaction force). Could you please help me clear this doubt?
For true acceleration, you need to go full general relativity...or at least 1st order. With that, local "g", which is Newtonian gravity plus Omega^2r, is what it is, and it's what an accelerometer measures. (This is why the most accurate models of Earth's gravity are CLASSIFIED, but EGM2008 is open and good enough for most people).
So we calculated the coriolis acceleration for each case of merry go round example. Does this coriolis acceleration remain constant throughout the trajectory of that ball? Actually I'm trying to plot a trajectory of a projectile at equator thrown eastwards seen from top down view of Earth (north pole) and I need to take coriolis force into account
F_cor/m = -2w X v. So in a plane, F_cor = -2mwv. (w=omega). There is ZERO position dependence. F_cent/m = w X (w x R), so F_cent = mw^2R. There is ZERO velocity dependence. (It is 100% not a coincidence that the Lorentz force on a charge: F =q(E + v X B) has a purely positional (electric) term and a purely velocity (magnetic) term).
(AA 516) Hi Professor, I am confused at 4:06 as to why it would look like the cannon ball is being deflected from the viewpoint of the star destroyer. It looks like the gunner can tell that the projectile is moving in a straight line, with the x-wing appearing to reverse out of the line of fire. Wouldn't you have to be the x-wing pilot to get the 'force deflect' effect?
Chris, good question. This is all a matter of perspective. The Star Destroyer gunner could see it from either point of view, how would they know if the X-wing was "reversing" or if the ball was being deflected. If there is no other references (like background scenery for example) and all they see is a black backdrop, either viewpoint is valid.
In case it is helpful, here are all the Flight Mechanics videos in a single playlist th-cam.com/play/PLxdnSsBqCrrEx3A6W94sQGClk6Q4YCg-h.html. You can support this channel via Patreon at www.patreon.com/christopherwlum. Please let me know what you think in the comments. Thanks for watching!
Absolute Toss!
Some smartass remark: The acceleration of the earth rotation vector can be assumed for your calculations to be the null vector, but actually it isen't exactly the null vector. Earth rotation is very slowly slowing down.
AA516: I appreciate how you touched on examples of different situations of rotating frames and how the velocity and accelerations are effected. This helped me see patterns on how the projectile motion in effected by rotation.
Absolutely wonderful. Here (finally), we find a TH-cam video lecture, which provides a balanced, qualitatively, and quantitatively accurate description and interpretation of the Coriolis and centrifugal acceleration components associated with rotating frames of reference. The examples are perfect.
Hi Michael,
Thanks for the kind words, I'm glad you enjoyed the video. If you find these videos helpful, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum. Given your interest in this topic, I'd love to have you a as a Patron as I'm able to talk/interact personally with all Patrons. Thanks for watching!
-Chris
AA 516: Great intuitive explanation of how the Coriolis and centrifugal acceleration terms come into play for a rotating frame. That's also a nice Bainbridge Parks Department "sun" you've got-I grew up on Bainbridge and even worked for the parks department as a summer camp counselor in high school (but never got my own beach ball...).
AE512: I like the artillery shell example. Very easy to grasp and illustrates the concept well. It's amazing how large the magnitude of the effects can grow as distances increase.
AA516: Great Lecture video Professor. All the examples with values shown are very helpful with wrapping my head around the motions seen from a body frame. I liked ALL the star wars references.
AA 516: Very helpful examples, it's a tricky thing to visualize.
AE512: Really handy buildup and breakdown of each term in the equation. Thanks!
AE512: I remember being very confused with this equation in my undergrad dynamics course, but now I feel like I actually understand it. Thanks for all the example cases
AE512: great follow up to the previous video showing the mathematics behind the forces on a merry go round!
The many clear examples gave me a much better understanding of acceleration in rotating reference frames
AE 512 Great lecture! Your explanation about the Coriolis effect provides a great insight on how weather patterns are affected on Earth.
Great video! The example cases are extremely helpful in illustrating the concept and dissecting how each of the components in the equation affect the true acceleration.
AE512: Definitely a long one, but the breakdown was easy to follow and the examples were very helpful!
What....A......Video. This thing was jam packed with the good stuff.
I think this is what finally made it click. Thank you so much!
AA516: Forgot to comment on this when I watched it the first time but the varied examples really helped me visualize these tricky concepts
AE512: Quite the expression for acceleration. Hard to believe there are that many terms. But at least they can all be identified and explicitly defined as something relateble!
AE 512: Beautifully explained. my Dynamics course from undergrad make more sense now :)
AA516: I was having a bit of trouble understanding how the accelerations worked out in the previous video with the playground carousel but looking at the vector math cleared alot of it up for me!
You are a magnificent teacher.
Great video! I really enjoyed how you included all those star trek references, those movies are great!
AE512: Hey Dr. Lum, thank you so much for making this: Heads up, I noticed a tiny typo on the whiteboard at 1:35:25 Where you write a_P/r = a_P/r + [Other terms] when its supposed to be a_P/b. You correct it in your next derivation step, but I definitely had to do a double take! Otherwise, fantastic video!
AA 516: Examples made everything much easier to make sense of physically
This was a great way to understand the coriolis and centrifugal accelerations!
[AE 512] 1:01:38
The visualization of the acceleration vector helped how the ball is affected by Coriolis. Usually I am a visual person but the mathematical/vector visualization actually helped me more.
Since you have acceleration, you could solve for the "force" using the projectile mass?
AA 516 - Great Lecture!!
great video ! Thank you Dr
I'm glad it was helpful. There are several related videos on the channel. Please feel free to check them out and I would love to hear what you think in the comments. Thanks for watching!
This is a great explanation!
AE512: @27:10 you talk about how the angular acceleration relative to r is equal to the angular acceleration relative to b. However, in the Coriolis derivation video I thought we defined that only to be true when we choose r_p/b to be equal to w_b/r... Perhaps you'll elaborate on this later in the video...
nice stuff, Dr. lum!
AA 516: Again, the perfect way to understand these concepts is in this video! Just a small typo at 1:31:56 I guess that made me a little bit confused there 😜 a_{P/r} = a_{P/r} + 2(...) +...
YOU ARE AMAZING!!!!
Great explanations and use of visual aids
AA 516: Hi Professor, this is a great video and very easy to follow! I do have a question though. I'm not sure if you have already answered this but for Case 2, shouldn't the a_p/r = [0 0 -9.81] and not the a_p/b term?
amazing explanation
Thank you very much for such an amazing video.
But one thing is hard for me to understand at 1:00:18, and that is a_p/r =[0 0 -g]'.
What I understood is that, a_p/r is the acceleration of vector p w.r.t to the reference frame. How are the first 2 terms zero? Because from the reference frame, observe can see that position has non zero acceleration in all 3 reference frame axis.
You said we live on a rotating sphere. Do you have a physical measurement of earth curve or earth radius? Also, why don't we observe an apparent deflection (Coriolis effect) of objects in the air as we observe them from the ground if earth is a non inertial spinning reference frame?
AA516: Professor, it's a great video as usual. So, the accelerometer measures using Earth as a reference frame and the plane as a body frame, is that right? (Name: Daniel Teshome)
Hi Daniel, good question. The aircraft is a typically the body frame but actually earth is not an inertial reference frame as it is rotating.
AE512: Appreciate the acknowledgement of the flat earth at 1:08:25 🙏🙏
AA516 I learn a lot, the first time to express coriolis effect mathematically. Po
AA516: Is it safe to say that the fictitious Coriolis Force and Centrifugal Force are sort of like torque in that they are zero when projectiles are moving along the axis of revolution?
AE512: I believe there's a minor error @1:05:00. Should be a_p/r not a_p/b
AE 512: Would the bullet land on top of you if you shot it straight up, and taking in the affects of air resistance?
Excellent
Shouldn’t the centrifugal acceleration at 1:06:20 be [-1.64 0 0]^T? Omega cross r in parentheses has a direction of y and omega cross y has a direction of -x
Edit: you just forgot the minus sign before the equation there, we are observing the motion from the frame b.
The only thing hard to believe about this video is that a cadet fresh out of the Imperial Naval Academy would be given such a prestigious assignment on a Star Destroyer. You have to prove yourself in the most disciplined Navy in a galaxy far, far away before making that kind of career leap.
Very good point. Perhaps he had some inside networking connections
not if your middle name is "Tiberius".
Hi,
Great stuff. at time 39.40, you said centrifugal acceleration. I think this term is commonly refered as centripetal acceleration. Centrigugal is an inertial force with a minus on the centripetal acceleration?
Great show Christopher! Do you teach physics or Calc? You have a knack for it.
AA516: At 1:07:38 , you say that as Edward steps off, the same effects are seen. The tangential velocity of his throw is not folded into the V vector. So when he is sitting on the ground, he throws it at some velocity v + v_tangent to make it the same throw? In this case, the ball has no idea that is has been thrown from the ground, because its velocity is the same as the throw from the edge. So the V vectors are the same, and you described how the P vector is just slightly different but not meaningfully. So the last question is - is our omega the same? I think it is because we are in frame b so regardless of where p is or what v is, we are still going to have the angular acceleration from our POV (not edwards, though).
I am also tripped up by leaving Edward behind as we rotate if he steps off. But I think it is just an intuition thing because we also leave behind the balls as we throw them (whole essence of this is how to quantify this leaving behind?) since our hands no longer apply the force to keep them spinning with b.
Hi MIles, ah I see your question, thanks for the timestamp. Basically, what I'm saying is that it doesn't matter if Edward is on or off the merry go round when he throws the ball. Both cause the ball to fly in a straight line from an inertial perspective. However for Brian who is rotating, he doesn't care if Edward was on or off the merry go round when Edward threw the ball, both cases produce the same motion from Brian's perspective.
AE512
ibraha5
Very interesting lecture. I have a question, since things weigh slightly less at the equator does that mean they consume less fuel for example Rockets and aircraft? Thanks
At 34:39, calling it "translational" seems incorrect, there can be rotation too. Some people simply call it "the acceleration of the origin of the moving frame" (relative to the frame of reference). But you are not the only one who use that term, is it through misuse of language ?
thanks for the lecture!
Jason-AE512: This video explain the answer for one question in the homework.
AE512: Very interesting.
Great lectures!
I have a question which can be applied to this and previous video:
For example at time 27:14, about the angular velocity vector/derivative , you write w_b/r = w_r/b is it mean that vector components of w_b/r equals to vector components of w_r/b and there no need to rotate ang. vel. vector between the different frames? or maybe it means that the ang. vel. vector is the same for each frame but has different coordinates?
Best Regards
Thank you for your material!
Hi Oleg,
Thanks for reaching out, I'm glad you enjoyed the video. Unfortunately I'm unable to respond to questions on TH-cam due to the sheer volume of inquiries that I receive. That being said, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum as I'll be able to answer questions there. Given your interest in the topic, I'd love to have you as a Patron as I'm able to talk/interact personally with Patrons. Thanks for watching!
-Chris
In Case 2 (minute 1:06:15) we find the acceleration terms with respect to the body frame, but what if we wanted to find them with respect to the inertial frame? We know from the intertial frame's perspective we would see the ball going down (without any deflection), but what would cause all those coriolis, centripetal, tangential, etc terms to become 0?
So in reference to u other videos with drone.... Which reference are we describing the P. And what does the Position vector of p in reference to R represent ( in terms of drone video
AA516 - Fantastic lecture! Just one question: at 1:50:50, why does the velocity vector of the artillery shell become V_P/r, instead of V_P/b like earlier?
Gary, excellent catch, that is a typo. I've added some notes in the description of this video to highlight this correction/errata. Thanks for keeping such a sharp eye out! Please let me know if you find anything else fishy in any other videos, thanks.
AA 516 I am wondering the effect of the fact that these projectiles are moving through a fluid (the atmosphere) which is also rotating at roughly the same rate as the earth body frame. Does this fact cause a damping effect on the predicted magnitudes of these coriolis accelerations?
Hi Joseph, you bring up a good point. The atmosphere is also subject to these forces (think about the hw problem about cyclones and hurricanes). That being said, the aircraft will experience local aero forces/moments due to moving through this fluid. It is just a matter of resolving the directions/magnitudes of these effects. We'll explore this during our discussion on wind tunnel testing.
AA 516: Celeste Yuan (Late due to name discrepancies discussed)
AE512: Now I can finally explain why there is no centrifugal force
Dr. Christopher, I had a doubt. First of all, Thank you for the amazing video series. My doubt was that at 2:11:32, you say that the accelerometer measures "True acceleration". So if that were true then the accelerometer placed stationary on the ground would measure "Omega^2*r" but the actual accelerometer reading is not "Omega^2*r ~ 0.0338 at the equator". I am confused. I read it on Wikipedia and it says that an accelerometer measures proper acceleration (Normal Reaction force). Could you please help me clear this doubt?
For true acceleration, you need to go full general relativity...or at least 1st order. With that, local "g", which is Newtonian gravity plus Omega^2r, is what it is, and it's what an accelerometer measures.
(This is why the most accurate models of Earth's gravity are CLASSIFIED, but EGM2008 is open and good enough for most people).
So we calculated the coriolis acceleration for each case of merry go round example. Does this coriolis acceleration remain constant throughout the trajectory of that ball?
Actually I'm trying to plot a trajectory of a projectile at equator thrown eastwards seen from top down view of Earth (north pole) and I need to take coriolis force into account
F_cor/m = -2w X v. So in a plane, F_cor = -2mwv. (w=omega). There is ZERO position dependence.
F_cent/m = w X (w x R), so F_cent = mw^2R. There is ZERO velocity dependence.
(It is 100% not a coincidence that the Lorentz force on a charge: F =q(E + v X B) has a purely positional (electric) term and a purely velocity (magnetic) term).
@@DrDeuteron than you
(AA 516) Hi Professor, I am confused at 4:06 as to why it would look like the cannon ball is being deflected from the viewpoint of the star destroyer. It looks like the gunner can tell that the projectile is moving in a straight line, with the x-wing appearing to reverse out of the line of fire. Wouldn't you have to be the x-wing pilot to get the 'force deflect' effect?
Chris, good question. This is all a matter of perspective. The Star Destroyer gunner could see it from either point of view, how would they know if the X-wing was "reversing" or if the ball was being deflected. If there is no other references (like background scenery for example) and all they see is a black backdrop, either viewpoint is valid.
[AE 512]: 1:06:53
I think a_{p/b} = [0 0 -9.81] has incorrect subscript. It should a_{p/r}.
[AE 512] Just saw that this gets covered at 1:37:57
feeling bad for the flat earthers .... by the way fun class sir
AE512: Came for the lecture, stayed for the Star Wars memes 😀
More to come in future videos 🙂
Hello Prof，one question: at 1:05:05 you wrote ap/b but I am confused why not ap/r?
I agree with you. It should be ap/r.
AA 516 - Allie S
A A 516: Ojasvi Kamboj
self note, not a comment:
skip this video and go to 7/29
Not "Giovanni Battista Rikkioli" but "Giovanni Battista Ri'choli". That is the pronunciation of Riccioli.
coool
AE512
0:20-lol. Sorry. No we don’t. Earth is stationary.
JAJAJ
First problem with pseudoscience: no direct empirical demonstration of claim. Why don’t you use a terrestrial example?
because it trigger flerfs.
💁
Comments...
Imagine teaching for more than 2 hours and realize the camera isn't recording...
I'm just here so I won't get fined.
U r wrong. I challenge u to a live debate. Dont ignore me
what you got?
@@DrDeuteron me got balls .
U sir ? 🤔