Maths/science genius needed

[hartech]

Can anyone help - my final uni year was the last time imperial units were used and there is a different notati0on used than I can remember from 50 years ago. So I want someone to calculate the answer to 2 questions for me that are defeating me at the moment. No great accuracy needed - ball park will do.

A flywheel of weight 30 lbs is rotating at 7000 rpm and has a diameter of 10". It rotates in line with the car CW from the rear. Gyroscopic precession would mean that if the car went round a CW corner the spin axis points forward and the couple would be pointing into the ground - so the front of the car would bed down on the suspension (I think)?

(1) What is the force trying to move the flywheel with gyroscopic precession downwards if the spinning flywheel is moved around a CW radius of 115ft in 3 seconds?

(2) If the car got in a spin (say CW again) and say it spun with the flywheel radius of 3ft at a rate of 1 spin in3 seconds what would be the force moving the flywheel downwards at that moment?

I understand the general principles of angular momentum and have managed to work out a few answers different ways but they doo not agree - and I don't mind the answer in lbs or kg but some help would be great - thanks.



Baz

[7Racer56]

hartech said:

Can anyone help - my final uni year was the last time imperial units were used and there is a different notati0on used than I can remember from 50 years ago. So I want someone to calculate the answer to 2 questions for me that are defeating me at the moment. No great accuracy needed - ball park will do.

A flywheel of weight 30 lbs is rotating at 7000 rpm and has a diameter of 10". It rotates in line with the car CW from the rear. Gyroscopic precession would mean that if the car went round a CW corner the spin axis points forward and the couple would be pointing into the ground - so the front of the car would bed down on the suspension (I think)?

(1) What is the force trying to move the flywheel with gyroscopic precession downwards if the spinning flywheel is moved around a CW radius of 115ft in 3 seconds?

(2) If the car got in a spin (say CW again) and say it spun with the flywheel radius of 3ft at a rate of 1 spin in3 seconds what would be the force moving the flywheel downwards at that moment?

I understand the general principles of angular momentum and have managed to work out a few answers different ways but they doo not agree - and I don't mind the answer in lbs or kg but some help would be great - thanks.



Baz

Hi Baz

The gyroscopic couple is a torque equal to I * We * Wp
I moment of inertia (1/2 m r^2 assume flywheel is a disc)
We (Omega e) engine angular velocity
Wp precession angular velocity due to turn/spin

Converting your figures into SI units I calculated 180Nm for both cases as the angular velocity is the same.
The vector of the couple is orthogonal to We and Wp so would tend to weight the front or back. Need to use right-hand-screw rule to work out direction easiest to search for 'gyroscopic couple' to see pics. There are some good references online I'll see if can find and post

You've also gyro effects from the wheel rotation...

Hope it helps - Jim

[hartech]

Thanks Jim, I do appreciate your help but I have managed to find that information already - what I am struggling with is to calculate the answers. It might be my age or unfamiliarity with the units - but I am really struggling with it (might just be thick!) you couldn't have a go at it for me could you - it would be much appreciated.

Best regards,

Baz

[7Racer56]

hartech said:

Thanks Jim, I do appreciate your help but I have managed to find that information already - what I am struggling with is to calculate the answers. It might be my age or unfamiliarity with the units - but I am really struggling with it (might just be thick!) you couldn't have a go at it for me could you - it would be much appreciated.

Best regards,

Baz

Here is the calculation of the gyroscopic couple with your numbers turned into SI units:

Flywheel of 10" has approx radius 0.125m weight of 30 pounds is approx 15Kg
So moment of inertia (1/2 m*r^2) = 0.5 * 15 * 0.125 * 0.125 = 0.117 Kgm^2
Flywheel rotates at 7000 rpm or 117 revs per second, multiply by 2 pi to get angular velocity in radians per second which is 735 rad/s
Precession angular velocity is 1/3 * 2 pi (one rev per 3 seconds) which is 2.09 rad/s

So the torque (I * We * Wp) is 0.117 * 735 * 2.09 which is 180 Nm

I did find a useful looking reference with car example which you might be able to use

https://books.google.co.uk/books?id=hVeaAL0j3T0C&a...

[catsey]

Not to drag this thread out but it was a great subject just shows how much i have forgotten Baz. I need to get back to my books i studied in 68/69 so all my exams had to have 2 answers Imperial and S.I. done with a slide rule my god where did all that brain matter go.
But reading your analysis of the bore scoring in my mind thats a top experienced all seeing engineer talking
good job Jim

[hartech]

Thanks for your help guys, it seems I was not quite as incompetent as I thought - seems to have puzzled most everyone else as well.

Anyway the help I have received has enabled me to establish that the gyroscopic forces can indeed contribute to crankshaft flexing and main bearing failure - which is what I was trying to prove.

All help was very much appreciated.

I had completely forgotten about slide rules - what was that all about and I wonder what our next generation would have made of them? LOL



Baz

[thebraketester]

Is 7Racer56 Walter Lewin in disguise?

[7Racer56]

thebraketester said:

Is 7Racer56 Walter Lewin in disguise?

Afraid not but I did study Physics and use maths/physics all the time in my work and hobbies

[catsey]

hartech said:

Thanks for your help guys, it seems I was not quite as incompetent as I thought - seems to have puzzled most everyone else as well.

Anyway the help I have received has enabled me to establish that the gyroscopic forces can indeed contribute to crankshaft flexing and main bearing failure - which is what I was trying to prove.

All help was very much appreciated.

I had completely forgotten about slide rules - what was that all about and I wonder what our next generation would have made of them? LOL

Baz

As can Thermal distribution of the block etc will cause crank deflection and undue stresses on the crank.however in the case of a short well supported crank the deflection would i believe not be an issue. Looking at the bore scoring issue which you relate to Cooling design my thoughts were how much the thermal distribution of the block impacts the crank deflection.

Edited by andy.mod on Thursday 15th March 15:01

[hartech]

Thanks Catsy but you seem to have attributed your last paragraph above to me whereas that comment is down to you.

The research behind the question I asked is about a bigger subject relating to the additional crankshaft overhang on the models we rebuild most often and the resulting effect on crankshaft stiffness when racing
them.

Baz

Edited by hartech on Thursday 15th March 10:50

Edited by hartech on Thursday 15th March 10:51

[catsey]

hartech said:

Thanks Catsy but you seem to have attributed your last paragraph above to me whereas that comment is down to you.

The research behind the question I asked is about a bigger subject relating to the additional crankshaft overhang on the models we rebuild most often and the resulting effect on crankshaft stiffness when racing
them.

Baz

Edited by hartech on Thursday 15th March 10:50

Edited by hartech on Thursday 15th March 10:51

my aplogies i was thinking aloud english not being my first language lancashire dialect being my first as Hilda Baker would say <im sat so im sitting"

[catsey]

catsey said:

my aplogies i was thinking aloud english not being my first language lancashire dialect being my first as Hilda Baker would say <im sat so im sitting"

no i get it no let me apologise that was a pure mistake my sincere apologies
wrongly submitted and edited reply again Baz my sincere apologies

[catsey]

hartech said:

Thanks Catsy but you seem to have attributed your last paragraph above to me whereas that comment is down to you.

The research behind the question I asked is about a bigger subject relating to the additional crankshaft overhang on the models we rebuild most often and the resulting effect on crankshaft stiffness when racing
them.

Baz

Edited by hartech on Thursday 15th March 10:50

Edited by hartech on Thursday 15th March 10:51

Baz i have requested moderators remove my reply