maximum piston speed? 11

[bigtomwcp]

in my quest for more useful knowledge i am wondering what kind of piston speeds are the limit? i know some of you guys out there deal in F1 and such. i had jotted a number on a small piece of paper an F1 guy told me a few months ago but i have misplaced it and it is important now. i think it was 28m/s or was it f/s? thanks for the help i am really looking for a max this engine will only run for 200 miles then be rebuilt. i am trying to maximize breathing with the best trade off of stroke and rpm.

 

[aorangi]

Formula 1 engines are actually around 26 m/s mean piston speed and 41 m/s maximum piston velocity at redline.

 

[Warpspeed]

Someone please correct me if I am wrong, but from what I have read, it it conrod strength that is really what limits piston speed, not the piston.

As I understand it, the greatest tensile stress in the rod is a TDC during the exhaust stroke, where there is no gas pressure to counterbalance the inertial loads. As a result the alternate tension and compression loads on the rod can quickly lead to fatigue of the rod, usually in the thinnest section just below the pin boss.

There is no real fixed limit. A lot depends on what the rod is made from, piston weight, and how long you expect it all to last.

 

[RobHughes]

I work for a company that races and sells high performance motorcycle engine parts...here's a post I put up on one of the enthusiast boards when people started talking about wanting to raise the redline of their bikes from 5K to 6K or more. FYI the bike is Yamaha's Warrior an air cooled V-twin that displaces 102ci stock and the connecting rods are scary long and skinny...lol


From the postings:

At 5000 rpm your piston goes from a complete stop to 66mph in 2 1/4 inches in just .003 seconds.

Interesting Warrior Engine facts/figures:

Engine RPM/ Piston Velocity mph/ G's exerted on rotating mass.
1000 / 13.25 / 40.49
2000 / 26.50 / 161.98
3000 / 39.76 / 364.47
4000 / 53.01 / 647.95
5000 / 66.26 / 1012.43
6000 / 79.52 / 1457.90
7000 / 92.77 / 1984.36

For Comparison at "redline":

Chevy 350
Engine RPM/ Piston Velocity mph / G's exerted on rotating mass.
6000/ 62.20/ 1140.15

Formula 1 engine
Engine RPM/ Piston Velocity mph/ G's exerted on rotating mass.
17,000/ 83.56/ 361.27

2004 R1 Engine
Engine RPM/ Piston Velocity mph/ G's exerted on rotating mass.
12,500/ 78.58/ 250.12

2004 R6
Engine RPM/ Piston Velocity mph/ G's exerted on rotating mass.
15,500/ 79.98/ 315.69

2004 V-Rod
Engine RPM/ Piston Velocity mph/ G's exerted on rotating mass.
9000/ 76.14/ 174.50

OK guys for those who are not bored by this...here's the math.

I did my math in feet, just to keep from having to change the numbers up at the end, but trust me it's the same.

Warrior Stroke=113mm or .370735 feet.
Distance traveled by crank per revolution 1.16632 feet (remember that the circumfrence is "pie"* diameter)
Revolutions per minute=5000.
Distance crank travels per minute=5831.608202 feet
Distance crank travels per hour=349896.4921 feet or 66.2682 miles per hour.

So if the crank shaft is traveling at this rate the pistons reach this max velocity twice per revolution at 9 o'clock and 3 o'clock since they are traveling at the exact speed that the crankshaft is, remember at 12 and 6 o'clock the pistons are "stopped".

To calculate the G-Force you have to take your revolutions per second (rps) which is 83.3333 (at 5K)and figure how long it takes for one revolution or .0120 seconds (1/83.3333). The piston goes from a dead stop at 12 o'clock to full speed (or 97.1934 ft/second) in 1/4 a revolution or in .0030 seconds. So the average acceleration in a second needs to be calculated or how many times per second does this event occur 1/.0030 = 333.333 times per second, now multiply this by the speed at full acceleration (97.1934*333.333) gives the figure of 32397.82 ft/second/second as the average acceleration. G-Force is 32ft/second/second. Divide 32397.82 by 32 to get the average G's exerted on the parts...or 1012.432 G's. Whew....if you hung with my math you deserve a gold star...lol

A piston weighs in at around 400grams, so at full G's right when it is stopping it "weighs" an astonishing 892.79 lbs!!!

The g's are exponentially related to the RPM and crankshaft length relationship. The Warrior crankshaft goes from 33mph at 2500rpms with 253G's to 66mph at 5000rpms and 1012G's. At 10,000 it would be 132mph with 4050G's.

The F1 crankshafts are, I forget exactly, but like 1.65 inches. Do the math Gotta, no scare tactics here, pure physics. I was just joking about the connecting rods, but it is something to think about when you start wanting to get a few more revs out of your bike.

This calculation has nothing to do with bore or weights in the calculations demonstrated.

Rob Hughes
Orient Express Powersports

 

[Warpspeed]

Wow, 133mm stroke eh !

That certainly is a man sized stroke on that Warrior. Makes the stroke on anything else look like just a bit of vibration.

 

[RobHughes]

Well close 113mm...still pretty big.

 

[76GMC1500]

Why would the g's on the Chevy 350 be so much higher than everything else? Piston speeds are slower, rpms are slower, so there is more time for the piston to reach its speed of 66mph. Oh, and when you calculate the force exherted on the rod by the acceleration of the piston, don't forget that the rod exherts a significant force on itself too.

 

[patprimmer]

For piston speed to be maximum at 3 and 9 "O" clock, you need an infinitely long rod, but the math to do this for a defined rod length is beyond me I must admit.

Your example will be within a few % of actual I expect.



Regards
pat pprimmer@acay.com.au
eng-tips, by professional engineers for professional engineers
Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

 

[RobHughes]

Woops...i just re-checked my math....

Chevy 350
Engine RPM/ Piston Velocity mph / G's exerted on rotating mass.
6000/ 62.20/ 1140.15

Formula 1 engine
Engine RPM/ Piston Velocity mph/ G's exerted on rotating mass.
17,000/ 83.56/ 4324.97

2004 R1 Engine
Engine RPM/ Piston Velocity mph/ G's exerted on rotating mass.
12,500/ 78.58/ 3001.46

2004 R6
Engine RPM/ Piston Velocity mph/ G's exerted on rotating mass.
15,500/ 80.89/ 3831.51

2004 V-Rod
Engine RPM/ Piston Velocity mph/ G's exerted on rotating mass.
9000/ 76.14/ 2094.07

Yikes...the math gremlins got in my excel program and jacked up my F1, R6, R1 and V-rod figures....sorry all.

4300+ g's....holy sheet batman.

 

[aorangi]

At 19'000 rpm, the maximum piston acceleration in a BMW P83 of formula 1 is 10'000 g .

http://scarbsf1.com/BMW_P83/index.html

http://forums.atlasf1.com/showthread.php?s=&threadid=61653 http://scarbsf1.com/BMW_P83/index.html

Cheers
Aorangi

 

[hfalex]

Hi everybody and sorry for my bad english.
I try to put my little experience here for my 1st post.

Main limit for the mean piston speed comes from an aerodynamic limit.
Since mps=IM x Cso x Cem x Ar/S

IM= MACH Index, which has a top limit of 0.6 (see graph on TAYLOR-the internal combustion engine in Thery and practice)-MIT-London
Cso= Air speed in normal conditions is 340m/s at sea level
Cem= mean efflux coeff.is 0.436 (F1 engines middle '90s)
Ar/S= geometric area of valves/area of piston is 0.3 (F1 engines middle '90s)

So, the resul for the limit of the MPS is 26,7 m/s.
More or less MPS of 27m/s is the actual limit in F1 engines.

Bye.
Alex

 

[GregLocock]

So to raise the mena piston speed it would be a good idea to increase Cem or Ar/S or both. I know where the choking limit comes from, is there an absolute limit to the others?





Cheers

Greg Locock

 

[NormPeterson]

Pat - try these:

InstantaneousPistonVelocity = -2*PI*(RPM/60)*(Throw/12)*(TAN(RodAngle*PI/180)*COS(CrankpinAngle*PI/180)+SIN(CrankpinAngle*PI/180))

InstantaneousPistonAcceleration = -(RodLength/12)*(COS(RodAngle*PI/180)*InstantaneousRodAngularVelocity^2-SIN(RodAngle*PI/180)*InstantaneousRodAngularAcceleration)-(Throw/12)*(COS(CrankpinAngle*PI/180)*CrankAngularVelocity^2-SIN(CrankpinAngle*PI/180)*BigEndAngularAccel)

All dimensions are in inches, angles are in degrees, angular velocities in rad/sec, angular accelerations in rad/sec^2. Outputs are in ft/sec for piston velocity and ft/sec^2 for piston acceleration.
BigEndAngularAcceleration allows input of crank rotational acceleration.

As a side note, the rather largish spreadsheet that I took the above from gives -2320g (at ~0.070* ATDC) and +1259g (at ~214* ATDC) for the maximum negative and positive maximum piston accelerations for a Chevy 350 at 6000 rpm with 5.7" rods and 0.020" piston pin offset. Maximum positive and negative piston speeds are 95.4 ft/sec (~286.01* ATDC)and -95.2 ft/sec (~74.47* ATDC) at that rpm. It also gives a 10000-ish number for peak g's for the BMW P83 engine.

I need to work on the ATDC angle lookups for the max values a little more, though.

Norm

 

[DesignOutsourcing]

Thanks Norm,

I'm surprised it took this long to reach the point about maximum acceleration. I always thought that the real issue is the maximum (not average) acceleration and the stress and fatigue this causes. One reason for longer rod ratios in high rpm engines is to reduce the max acceleration at TDC (there are also benefits from being near TDC for longer and better rod angularity during the combustion stroke.)
I found some interesting piston kinematic spreadsheets on this page (and page 2.)

http://e30m3performance.com/tech_articles/engine-tech/rod-ratio/

Saw an F1 piston at the Mahle stand at Automechanika last month and it was extremely short. The height reduction seemed limited by the pin diameter. The pin length was about half the piston diameter to reduce weight.

cheers, derek

 

[notnats]

Without looking up any references, and ignoring offsets, isn't the maximum piston and conrod acceleration the same as the centripetal acceleration of the crank pin?

ie
omega squared . r

At TDC and BDC all the elements are in a straight line and accelerating in the same direction

Jeff

 

[NormPeterson]

Piston motion is not simple motion. What you're saying is probably true in Pat's infinitely long rod engine (see his March 24 post above). I hadn't added a centripetal acceleration check to the spreadsheet, as it didn't seem to have much significance. But if I make the 350 SBC rod length something silly like 1E6 inches the magnitudes of the maximum positive and negative accelerations become equal (at +/- 1777.8g for 6000 rpm). Basically what that does is to make the rod angular velocities and accelerations negligible so you'd be looking at only the crankpin effect.

Without attempting a rigorous derivation, decreasing the angularity of any given rod has the effect of raising the piston in the bore while increasing its angularity has the opposite effect. So as you approach TDC both effects are raising the piston. After TDC, both are lowering the piston. Approaching BDC, the crankpin motion is lowering the piston while the reduction in rod angularity is raising it. After BDC the crankpin raises while rod angle lowers. Hence, taking these motions as velocities and differentiating for acceleration would be expected to show asymmetric TDC vs BDC results as well.

It's perhaps interesting as a side note that for most common rod:stroke ratios there are two relative maximum positive accelerations and (assuming zero pin offset) that the acceleration at BDC is a relative minimum (although still positive). You have to get up to about a 6.6" conrod on that 350 for a single maximum positive acceleration to occur at BDC.

Norm

 

[NormPeterson]

Just for clarity,

as you approach TDC both effects are raising the piston

the two effects are
(1) crankpin movement, and
(2) change in rod angularity

Norm

 

[strokersix]

Maximum piston velocity should be at the points where the connecting rod axis is perpendicular to the crankpin to main journal axis. In the limit of infinite rod length, this is 3:00 and 9:00.

I must confess I did not plug into the formula but logically this must be true.

 

[ivymike]

InstantaneousPistonAcceleration = -(RodLength/12)*(COS(RodAngle*PI/180)...

Interesting approximation. That's based on the "piston motion is a combination of a sin and a cosine" approximation, right? How does that compare to a precise calculation? As I recall, it's off by a couple of percent in a few places.

Piston axial acceleration (kinematic, closed-form solution for constant crankshaft angular velocity):
-a*cos(o)*w^2 + (a^2*w^2) * (1-2*cos(o)^2)/(sqrt(r^2-a^2*sin(o)^2) - (a^2*sin(o)*cos(o))^2*w^2)/(r^2-a^2*sin(o)^2)^1.5

where
a = crank throw
r = rod centers length
o = crank angle in radians
w = crank angular velocity in rad/sec

The above is based on taking two derivatives with respect to time of the formula for piston position:
position = a*cos(o)+sqrt(r^2 - a^2*sin(o)^2)

I can provide a (more complicated) version if you want to include pin and crank offsets from the cylinder axis, or crankshaft angular acceleration.

 

[doejohn]

Here's some equations for piston kinematics I had worked out some time ago. They might even be correct!

let r = rod ratio = (length conn rod)/(stroke)
let ? = crank angle from TDC
let ? = d?/dt = engine speed (radians/time, not rev/time)
let u = piston position from mid-stroke)
let ú = du/dt = piston velocity
let ? = d²u/dt² = piston acceleration
let ? = 2r
let ? = (?² - 1 + cos²?)^½

And first note that for infinitely long conn rod (r=?), piston motion approaches sinusoidal, where
max u = a
max ú = a?
max ? = a?² for constant engine speed (d?/dt = 0)

Actual motion for pistion (finite conn rod length) can then be expressed as ratio to max sinusoidal motion:

u/a = -? + ? + cos?
ú/a? = -sin?[1 + (cos?)/?]
?/a?² = -(cos? + [(sin²?)/?]•[(cos?)/? - 1])•[(cos?)/? - 1]

These normalized motion equations approach sinusoidal for larger rod ratios, with max/min values of ±1. The amount that the normalized velocity and acceleration max/min values exceed ±1 represent the amplification due to non-infinite conn rod length. Again, engine acceleration was neglected in deriving normalized acceleration equation.

Note that maximum piston acceleration is amplified over sinusoidal max (a?²) by factor of (1 + 1/?) = (1 + ½/r). Trends pointed out by Norm above can be seen (what's with the Structurals hanging out here?....)

FWIW, I've heard max piston accelerations for near-current F1 engines as being around 10,000g, as mentioned above. Same source reported engine accelerations of 25,000rpm/sec.

 

[doejohn]

Whoops,
Looks like some fancy characters that showed fine in "Preview" of my post above didn't survive actual posting! They all turned into question marks!

I hope to repost with corrections later...