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Is odd better than even?
4

Is odd better than even?

Is odd better than even?

(OP)
Another engineer and I were discussing a design for a manifold and how many parallel channels we should use in this manifold.  The other engineer said an old timer once told him to use odd numbers whenever possible when designing things.  He said that is why most wheels have an odd number of spokes.  The old timer didn't explain why odd numbers are better.  I've seen many designs using even numbers and they seem to work fine.

Has anyone else heard this? Does anyone have an idea why odd numbers of things might be better than even?

Phil

RE: Is odd better than even?

Floral arrangers like odd numbers.

RE: Is odd better than even?

Don't ball and roller bearings generally have an odd number of elements?  Will be curious to see others input on this one.   

RE: Is odd better than even?

Is this why a baker's dozen is 13?

RE: Is odd better than even?

halfway from being too much or too little?

Tobalcane
"If you avoid failure, you also avoid success."  

RE: Is odd better than even?

It may be a slight modification of the "Goldilocks Principle" LOL
In the case of car wheel lugs or nuts, 4 seems too little, 6 seems too much, 5 seems just right.  

When increasing the load capacity of the wheel, the number of lugs or nuts goes to 6, or on up to 8, & sometimes 10 but I've never seen a 7-hole pattern used for this; odd, eh? (no pun intended)

Also, it could be a harmonics thing.  Odd numbers would be less likely to set up harmonics, such as number of balls in bearings.

If at all possible, gear trains and PD belt assemblies are usually made up of odd numbers of teeth or a combination of odd/even that allows "hunting", so that wear is maximally spread.

 

RE: Is odd better than even?

I believe 3,5,7, etc ribs on a casting or weldment, for example, will allow it to stress relieve (move) better than 2,4,6 etc ribs will because they are not diametrically opposed. It is also sometimes recommended to have unequal spacing between the ribs.  

RE: Is odd better than even?

Odd is better than even for (4-stroke) radial engines for reasons of timing.

- Steve

RE: Is odd better than even?

Good discussion, always enjoy hearing what jewels of wisdom "old timers" have to offer.

I would go along with RebelBrill.  It would seem logical one would want to avoid any sort of "diametrically opposed" construction, whether it's mechanical or some analogous situation.  It would indicate the reason would be due to induced harmonic tendencies manifesting in a variety of ways, structural weakness, perhaps easier manufacturing,...whatever.  But always it seems the end result is designed-in robustness.

TygerDawg
Blue Technik LLC
Virtuoso Robotics Engineering
www.bluetechnik.com

RE: Is odd better than even?

In radial geometries, 7-pattern is not practical as that introduces "directionality" in the product. If you have to go odd, go with 3, 5 or 9 as it is easier to divide 360° that way.

I once stirred up a small storm when I tried to put 7 holes in a part to avoid lining up with 4 pins on a mating part (4 holes would have been too few, 6 or 8 holes would be liable to line up with 2 diamterically opposed pins simultaneously). I did end up putting 7 holes, but I know better now. I should have gone with either 5 or 9 holes.

That being said, I agree with tygerdog and RebelBrill. Cheers ...

RE: Is odd better than even?

On jet engines it is desirable to have a prime number of blades on disks, and also a prime number of vanes on the adjacent stators. By doing this one can minimize aerodynamically induced resonances. It's a target rather than a hard and fast rule. If there are ball-races nearby then it is also worth having carefully chosen numbers of bearing elements.

It's to do with 'aliasing'

 

RE: Is odd better than even?

Wheel spokes ,trolley wheels, sheave pulleys,centre ribs are always odd in number and I have preferred them too. There is a break in symmetry during stress relief,thus minimising distortion or cracks.

If they are cast parts and during cooling of the castings in the molds those with even numbers are found to crack near the hub. Thus in the case of odd members too,we do not provide straight elements but have curved ones.

I have not failed. I've just found 10,000 ways that won't work." — Thomas Edison
_____________________________________
 

RE: Is odd better than even?

"Odd is better than even for (4-stroke) radial engines for reasons of timing."

It's not just better, it's required! (And realize that rotary engines with an even number of cylinders have two rows of an odd number of cylinders - essentially two stacked engines.)
------------------------
"Is this why a baker's dozen is 13?"

Per Wikipedia (and other various sources): The oldest known source and most probable origin for the expression "baker's dozen" dates to the 13th century in one of the earliest English statutes, instituted during the reign of Henry III (r. 1216-1272), called the Assize of Bread and Ale. Bakers who were found to have shortchanged customers could be liable to severe punishment. To guard against the punishment of losing a hand to an axe, a baker would give 13 for the price of 12, to be certain of not being known as a cheat.

--------------------------
When designing gears or sprockets you should have at least one with an odd number of teeth the maximize wear. When both gears are even not every tooth with mesh with every other tooth of the second gear. It is similar for sprockets, where a roller element will not engage every tooth.

ISZ
 

RE: Is odd better than even?

ISZ,

Radial engines? Rotary engines passed into history a long time ago.

Interesting re. the Baker's Dozen.
  

----------------------------------
  
If we learn from our mistakes I'm getting a great education!
 

RE: Is odd better than even?

Maybe defunct, but still loads more interesting than a vanilla I4.  I shudder when I see pictures and videos of the JRL Radial Flyer (7-cyl radial-engined motorcycle).

http://www.youtube.com/watch?v=GUx35zuI5GI

I guess it's no more idiotic than a flat or boxer 6 and probably handles similarly.

- Steve

RE: Is odd better than even?

Rock. Paper. Scissors.

Always a tie breaker.

RE: Is odd better than even?

Bicycle wheels are carefully optimised, and they have even number of spokes. Possibly they have so many spokes that odd vs even is subordinate to the difficulty of indexing odd numbers.
 

Cheers

Greg Locock

SIG:Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips.

RE: Is odd better than even?

(OP)
I appreciate all the interesting responses.  It sounds like there is some engineering logic behind the statement, at least in some applications.

Skywalker09, I'm not sure I understand the concept of seven creating directionality.  Can you explain more?

Phil

RE: Is odd better than even?

Most of the real reasons that us "old timers" have these rules of thumb are lost in the mists of time.  Some of them are actually about fear and superstition instead of engineering, but some of them developbed because some smart guy observed that one configuration worked and another didn't.  Occasionally, the profession just uses the rules that work without ever working out the arithmetic of why "a" works better than "b".  This is ok except when the rule masks a "c" that is actually better than "a" or "b".  

Maybe somebody noticed the "prime number" case above and since all primes after 2 are odd, it evolved into "use odd numbers" even though many of the odd numbers are not prime?

David

RE: Is odd better than even?

I'm just coming round now...

- Steve

RE: Is odd better than even?

Symmetry and harmonics have similar roots.  In summing sine waves, odd numbered waves tend to cancel, even numbers to add.  Three-cylinder piston/plunger pumps have a theoretical output "ripple" of about 13%, 4-cylinder pumps have nearer 50%.

RE: Is odd better than even?

When the numbers gets large, it probably makes little difference.  For bearing designs under slow revolutions,
we maximize the number of rolling elements either odd or even.  I know that in some early designs of tapered roller
bearings for helicopters, the cage used differential spacing to help reduce the amplitude but I do not remember any even or add requirement.  

RE: Is odd better than even?

Odd is better in wheel design/manufacturing.  By not having an even number of spokes, any distortion from sub-par heat treat and quench, and stress relief after machining is reduced.  When i was in the industry, I justified it as "off-axis stress in cornering fatigue" to my counterparts, by stating that adding one spoke to an even spoke design increased the likelyhood of having at least one spoke close to being in pure tension or compression at any time (just a reason to add a spoke, thin down all of the spokes, and reduce the weight of the wheel, thus reducing unsprung weight).  Some battles were won, some lost due to cosmetic aesthitics, but FEA usually proved odd was better "lighter, stronger, truer".  

RE: Is odd better than even?

PhilBW,

Using prime numbers (for things like numbers of teeth on gears, etc.) is more beneficial than simply using odd numbers.  Prime numbers of gear teeth are less likely to produce coupled frequencies within various shafts in a driveline.

Other things like aircraft propellors, helicopter rotors, or turbine engine compressor/turbine discs might benefit from odd number symmetries if they are subject to vibration/turbulence due to passing frequencies.  And for noise sensitive applications, radial assymmetry is also sometimes used.

As for using odd numbers of elements for things like rolling element bearings, the exact opposite is usually  true, but for very practical reasons.  Cylindrical roller bearings typically have even numbers of rollers.  The reason for this is so that the square (or rectangular) retainer cage pockets can be through-broached.  With ball bearings, the number of balls in a deep groove or Conrad bearing is dictated by the max number of balls that can be accommodated by the assembly procedure used.  Angular contact ball bearing numbers are limited by how many ball can be fit around the race pitch circle.

Regards,
Terry

RE: Is odd better than even?

This is a fascinating thread!  I've been counting things for the last couple of days, looking for odd/even numbers, primes and (here's where things get really sad) Fibonacci numbers.

- Steve

RE: Is odd better than even?

I posted this a while back, but here's an example of irregular spacing of fan blades to reduce tonal noise

http://www.geocities.com/greglocock/fanblade.png

red is the original (calculated) spectrum, blue is with the blades still correctly positioned for balance, but staggered to reduce the tonal content at 5th order.



 

Cheers

Greg Locock

SIG:Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips.

RE: Is odd better than even?

GregLocock,

Here's an irregular spacing of blades on a tail rotor for noise reduction:

RE: Is odd better than even?

Odd numbers are better for items that are paired, like your fingers or toes. I'd much rather have an odd number of fingers on each hand.

RE: Is odd better than even?

Well, now you've revealed your bias against the Simpsons -why?

Fewer than two fingers and a thumb seems cumbersome, but 4,5 or 6 dactyls seem more like an aesthetic choice than a rational one (perhaps I am biased, my little fingers aka pinkies are effectively non functional these days)  

Cheers

Greg Locock

SIG:Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips.

RE: Is odd better than even?

I always liked Ned Flanders-until he got gang probed by the aliens.

RE: Is odd better than even?

Fun thread.

Bicycle spokes were brought up earlier as an exception to the odd better than even thing.  These are paired evenly because each spoke on the left side of the wheel is paired with one on the right side of the wheel, so that you can adjust the tension on each side in the vicinity of each spoke, thus truing a wheel.  That maintenance seems a lot more important than minimizing noise or vibration under the circumstances.

Well, I'm off to go count fan blades now.  Cheers.

RE: Is odd better than even?

AlyB, well, true, but that does not imply an even number of PAIRS.

Regards,

Mike

RE: Is odd better than even?

KENAT, I second that, this is a most interesting thread.

RE: Is odd better than even?

oh man, the shark has been jumped.

take the "4-wheeled" vehicles which are so popular these days... in reality, they've got an odd number of wheels (once you count the steering wheel), or you could simply say that they've got one set of wheels, one being an odd number.
 

RE: Is odd better than even?

ivy, if you're counting the steering wheel, don't you have to count the spare, which brings you even again unless your car only has a can of fix-a-flat.

I've been thinking about helicopters & even props and there's quite a mixture of odd and even even though you'd expect some of the dynamics issues to come into play.

KENAT,

Have you reminded yourself of FAQ731-376: Eng-Tips.com Forum Policies recently, or taken a look at posting policies: http://eng-tips.com/market.cfm?
What is Engineering anyway: FAQ1088-1484: In layman terms, what is "engineering"?

RE: Is odd better than even?

Since the car is not designed to rotate, the number of wheels is irrelevant to this discussion.  Just as the number of spokes is less relevant than the number of pairs of spokes.

Rules like this should be rigerously developed and published.  It seems that it is pretty common to have an odd (or prime) number of structural elements on a rotating shaft, but from the above none of us has described the reason why.

David

RE: Is odd better than even?

oh, my bad, I didn't realize we were talking about rotating manifolds.

RE: Is odd better than even?

I seemed to be developing that most of the interesting examples were rotating elements.  The number of wheels on a vehicle didn't seem germane.  Maybe it was me that was bad.

David

RE: Is odd better than even?

Just thinking about it a lot of splines are odd numbers of teeth as well (sometimes we use different odd numbers at each end of a shaft if we want really subtle adjustability).

The wear/phasing argument can't apply to a spline, is it just that gear makers habitually use odd numbers?

 

Cheers

Greg Locock

SIG:Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips.

RE: Is odd better than even?

my head hurts

RE: Is odd better than even?

well, you've only got one..  works well enough for everyone but Zaphod Beeblebrox.  Another odd winner.

RE: Is odd better than even?

Go for prime, every time.
But remember that the cicadas got there first, with their life cycles.

RE: Is odd better than even?

Horizontal axis wind turbine blades.  Never an even number, usually three.  There is a very simple technical reason for this.  You don't want a design were there are opposed blades - one lightly loaded in the tower shadow and one heavily loaded high up in the faster air.  Cyclic stress loading and all that.

- Steve

RE: Is odd better than even?

Excellent and entertaining discussion (that comment about the Simpsons was hilarious).

As for using prime numbers for gear teeth, this is always done unless there is a need for a specific ratio like that of a timing gear.  The reason is two-fold.  First, prime numbers of gear teeth are less likely to produce vibration problems due to coupled meshing frequencies.  And second, mating gears with different prime numbers of teeth give the best results for even wear.

Splines don't really care about the number of teeth, since they are rotationally coupled.  If your quill shaft needs a vernier feature for indexing, that is best accomplished simply by using a one tooth difference from one shaft's end spline to the other.

And with regards to the topic of rotor blade symmetry, how about a single rotor blade:



Regards,
Terry

 

RE: Is odd better than even?

prime numbers for gear teeth, this is always done

Always done... where?  I can't recall a single example, and I've been around for a number of engine geartrain designs at several OEMs.  I can't recall prime numbers ever coming up, although hunting teeth are good for a fight - they'll even out wear, but prevent thorough validation of the geartrain in a reasonable period of time.  As I recall, the number of teeth on each gear was usually defined by the rough geartrain centers layout, the desired pitch and contact ratio, and the desired (approximate) drive ratios.
 

RE: Is odd better than even?

I suspect a lot of the 'old timer's' rules came from the horse and buggy days when the wheels were wooden and so were the spokes.  With even numbered spokes, placing a couple of spokes at the high end of their length tolerance opposite each other would guarantee that the 'lower tolerance' spokes would be too loose to fit.  Odd numbered spokes would prevent that.  Wheel out of roundness probably wasn't a show stopper in those days.

Same principle applies to rollers turning inside a circular path, such as heat exchanger or boiler tube rollers, not that there aren't 4 roll tube rollers out there but the ability to center up the mandrel and evenly load all the rollers is much better in a odd numbered tube roller than an even numbered roller.  I would think, but can't state it that the same would be true for similar devises like some bearings.

rmw

RE: Is odd better than even?

A simple example of odd /even is 3 leg stools/chairs are better than 4 leg.   

RE: Is odd better than even?

That's because we live in three dimensions though.  A 5 leg stool would be over-constrained (wobbly) too.

- Steve

RE: Is odd better than even?

Artisi,

Three legs are better than one or two legs too...
  

----------------------------------
  
If we learn from our mistakes I'm getting a great education!
 

RE: Is odd better than even?

so how about the animal kingdom? seems like pairs of limbs are pretty common. allows some redundancy, but with minimal waste, perhaps?

RE: Is odd better than even?

So. Is zero odd or even?

 

RE: Is odd better than even?

SomptingGuy

Have you noticed how many rollable office chairs have 5 legs?  Much more stable than 3 or 4; doesn't tip over anywhere near as often.

Patricia Lougheed

Please see FAQ731-376: Eng-Tips.com Forum Policies: Eng-Tips.com Forum Policies for tips on how to make the best use of the Eng-Tips Forums.

RE: Is odd better than even?

Poo!! I wrote that last message sitting on a five-legger.

I was also told today that 3-bladed wind turbines were more prevalent because of their aesthetic not engineering attributes.

Prime numbers for gear teeth though still seems in the running.

- Steve

RE: Is odd better than even?

vpl,

That is true but only because most office floors are, to a reasonable approximation, two dimensional planes. A five legged chair on an uneven surface will almost always rock, while a three-legged one will almost always find a point where the three legs touch the ground.
  

----------------------------------
  
If we learn from our mistakes I'm getting a great education!
 

RE: Is odd better than even?

Scotty, unless you've got extreme irregularities, like the hole on a golf course, or an extreme angle such that C of G is an issue, a three legged stool or chair should never rock.  

How level the seat is is another matter.

I double checked on the way home Friday, lots of 2 blade wind turbines in the Santa Paula/Fillmore area of CA.

KENAT,

Have you reminded yourself of FAQ731-376: Eng-Tips.com Forum Policies recently, or taken a look at posting policies: http://eng-tips.com/market.cfm?
What is Engineering anyway: FAQ1088-1484: In layman terms, what is "engineering"?

RE: Is odd better than even?

Kenat,

That's the reason for the 'almost' qualifier in my comment - if the surface is at a sufficiently steep angle then the stool will tip beyond its balance point and none of the legs will touch the floor.
  

----------------------------------
  
If we learn from our mistakes I'm getting a great education!
 

RE: Is odd better than even?

looking at "manifolds"
for auto engines they are mainly 4,6,8,10,12,16, etc
for steam turbines are 2,4,6, and 8

RE: Is odd better than even?

That's because "manifolds"  are stationary - split evenly (usually, as in turbine casings) between the top and bottom of the two casing halves to evenly suck air from the rotating turbine blades.   

The simplest division is two outlets (one above and one below) but that tends to create "bubbles" or surges in the delivered gasses.  4 connections is better since that gives nice even fixed nozzles every 90 degrees: 45 up and down from the split line.   The more the connections to smoother the pressure.

RE: Is odd better than even?

I'm waiting for e & pi to enter the conversation!  How about the golden number.

RE: Is odd better than even?

Golden number already hinted at: fib(N)/fib(n-1) where n is large.

- Steve

RE: Is odd better than even?

Quote (Artisi):

A simple example of odd /even is 3 leg stools/chairs are better than 4 leg.  

   Are you suggesting that a tripod works because it has an odd number of elements?

Quote (IceStationZebra):

When designing gears or sprockets you should have at least one with an odd number of teeth the maximize wear. When both gears are even not every tooth with mesh with every other tooth of the second gear. It is similar for sprockets, where a roller element will not engage every tooth.

   Perhaps you are thinking of a hunting tooth?  Instead of meshing a 40 tooth gear with a 20 tooth gear, you would change the big gear to 39 or 41 teeth.
 

               JHG

RE: Is odd better than even?

It's not odd or even.
It's 1.6180339887......

peace

Fe

RE: Is odd better than even?

"Instead of meshing a 40 tooth gear with a 20 tooth gear, you would change the big gear to 39 or 41 teeth"

As you would if you were a gear manufacturer, and observe in passing that it is the lack of a common factor that is important, rather than primeness as such.

Cheers

Greg Locock

SIG:Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips.

RE: Is odd better than even?

yes, as I mentioned above, the hunting tooth is good for a fight.
 

RE: Is odd better than even?

Even if odd is better than even, I find it odd that even the Odd "Couple" was even.

RE: Is odd better than even?

WolframAlpha has the golden section shown as

-2sin(666°)

THere is a hidden message here I'm sure.

- Steve

RE: Is odd better than even?

Quote (GregLocock):

... As you would if you were a gear manufacturer, and observe in passing that it is the lack of a common factor that is important, rather than primeness as such.  

   Nor does the oddness or evenness matter.
 

               JHG

RE: Is odd better than even?

Yes, Steve got it. It's not odd or even it's evil wink

Fe

RE: Is odd better than even?

"Even if odd is better than even, I find it odd that even the Odd "Couple" was even"

Impressive and original!  That's the second most insightful post I've ever read on this website.

As for the original question regarding whether, in general, is odd better than even when designing something?  The answer is: It all depends upon the application.

Most religious types would agree that God is the ultimate designer.  And most men would agree that his best piece of work is the female body.  She has one mouth, two eyes, one belly button, two big toes, and one heart.  Odd, even, odd, even, odd, etc.  Can any of you think of a more perfect design?

 

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