"Column of Air" Scoop Sizing Hypothesis - Another Approach!
One of the Land Speed Racers, Richard (Rich) Fox, contacted me about an alternative way to find the appropriate scoop size. I looked it over and I feel that it is worthwhile to post this method as well as the other one. It turns out that they are actually the same, just re arrainged parameters and some simplifying. Rich commented
"that the formula came to him from Bones or Charlie Markley some years ago. At that time they were using a mile long column of air and the number of revolutions turned in one mile. I just shortened it to one revolution of the tire to deal with smaller numbers. It's all the same using speed and gear ratio to end up with revolutions of the crank or pi X tire dia. to get to the same place. I'm just trying to simplify things."
Rich, GOOD JOB!
Like the method that follows this one one the analyses index page this also only provides the scoop size for the engine turning at it's highest. While it does not look this way, tiz because you gotta change the overall gear ratio when at speeds less than max. The cautionary note that follows is the same as the other method.For any speed less than the target speed and at WOT the scoop size is too small and unmentionable things may happen to the motor, especially if using a carb which depends on air flow signals to meter the proper amount of fuel. I will develop the formula for sizing your scoop which will need only your engine displacement, an estimate of the engine volumetric efficiency, and the target speed you seek. Examples of the scoop size being too small will also be developed in examples.
Remember, I do this for fun and the value to you, the racer, fan, or whatever is worth only what you put on it. Should you use this formulation, I would like to hear of your experiences.
1) Engines are air pumps
2) CFM of air injested for a given RPM is constant
3) Displacement of your engine is known
4) You know your final gear ratio
5) You know your tire diameter
Remember, these are academic exercises and are ment for fun. There are so many variables that something will always be just a tad off. It is not intended to be a definitive answer to anything except our curiosities. To that end, if you find it useful, amusing or down right distasteful,GREAT! You may find errors, wrong assumptions, or other nastiness and I will appreciate you pointing them out to me. Complaints should be backed up by real data, through either analyses of your own or documented information. I am ameniable to changing my thinking iffn there is good reason to. Opinions, by themselves, just don't cut it.
Rich's Method as passed along by Bones or Markley (with example numbers)
1) The number of engine revolutions per revolution of the rear tire is equal to the final drive gear ratio,for example 2.5:1
2) Example engine displaces 400 cubic inches, so the amount of air per revolution is 200 cubic inches
3) The amount of air needed is 200 times 2.5 revolutions = 500 cubic inches [see note below]
4) The tire circumference advances you by PI * Dia of tire = 3.1416 * 28 = 87.96 inches
5) Dividing the air need by the advancement = 500 / 87.96 = 5.68 square inches
[Note] If you know the volumetric efficiency of your engine, then multiply that efficiency number by the amount of air injested. You do this because no matter how hard you try the air flow system (valves, ports, runners, gaskets, etc) will only let this amount of air into the engine. Dividing the air need number fools you into thinking that if you make the scoop bigger it will correct for the losses caused by bad volumetric efficiency numbers. Doesn't happen that way, I'm afraid. So if you were running at 90% VE your scoop should be 5.68 * 0.90 = 5.11 square inches.
I worked the example car I used in the other method backwards to see if it would yield the same results.
What I did...
1) Given the RPM, target speed and an assumed tire diameter, I found that the final drive ratio was 2.78:1
2) The example engine displaces 370 cubic inches, so the amount of air per 2 revolutions is 185 cubic inches
3) The amount of air needed is 185 times the 2.78 revolutions = 514.3 cubic inches. At 90% VE = 514.3 * 0.9 = 462.87 cubic inches
4) Dividing the air need by the advancement per rev of tire = 462.87 / 87.96 = 5.26 square inches
The other method gave 5.25 square inches, so I'll blame the difference on rounding in my calculator.
I wish to thank Rich Fox for sharing his method with me. I asked him if it was alright to share it with everyone and he agreed. Isn't this what it is all about? Fellowship, good friends helping other friends and everyone having as much fun as they can stand? Thanks, again, Rich. Tell Bones and/or Markley also...
This has been a serious effort to try and determine how big a scoop needs to be to meet a given speed requirement while minimizing drag. During the analysis it was found that scoop size for a given speed and engine conditions can be determined. but that this scoop size is inadequate for slower vehicle speeds at the same given rpm. As a get off the stage commentary, I would suggest that the very best air intake system can be found on the NASCAR Winston Cup cars: the inlet is at the base of the windshield and is a very large opening. Since it is in stagnant high pressure air, no penality for drag is observed, plus you get a bit of a boost! I would futher comment that the scoops which have the opening against the glass but which are also very tall are further insulting the air flow problem because the high speed air over the top of the scoop is actually sucking the air from the scoop, not the other way around. Point that puppy into the wind, boys! If you use this or a similar technique or the same methodology, just remember, your milage may vary :^}.