… solution by reading from a scale

[WebPilot]

 I've always had a certain fondness for graphical solutions to engineering problems. Several (5) years ago I posted Dimensionless Space and Time, which was a graphical solution to the one dimensional compressible flow problem due to what is known as the Kadenacy effect.

 Here is something I've engineered and drawn to estimate the thrust and exhaust diameter relation in a pulse-jet. Knowing the one, you can estimate the other by using this.

 Presently, you need to take the square root (√) of the d² value from the scale for a certain thrust level. You'll need tables, a slide rule or a calculator to do this. I plan on eliminating the need for this, shortly.

[WebPilot]

(c.t.)

[WebPilot]

 I've added a 2nd inner ring today, which allows the user to determine the diameter directly from the chart.

(c.t.)

[WebPilot]

 To use this 'device', you can use the file 'as is' in a graphics program, draw a line from the center extending all the way out, ensuring that it crosses the thrust or diameter value in question. Then it's just a matter of reading the scales.

 A second way is to print the plot out on card stock. Press a pushpin or thumbtack through the center and attach a piece of thin string or thread to it. Pull tight and cross the values in question. I like this latter method: no batteries, no computer, no software.

 An alternate second way is to print the plot out on card stock and use a transparent straight edge (scale or rule or drafting triangle) for the lines.

 

[WebPilot]

 I am working on a practice sheet for those of you who may be interested in learning how to use this.

[Kool]

That would be very interesting, I follow your topics with great interest, however it's sometimes over my head

[WebPilot]

 Ok, p², this will be time 'well spent'. I like this technique so much that I think I'm going to use it more often in the future.

 Here is the image we will be using for example purposes. I've taken the original wheel, loaded and cropped it in graphics program, and drawn 3 lines from the center to where you now see.

[WebPilot]

 We will begin with the Dyna-Jet.

 Looking at the outer ring, the inner scale is thrust. Locate the long line marked 0 and the next longish line marked 10. Halfway between is 5 (unmarked) and this interval has been divided into 5 parts. I drew the line from the origin to the 4 mark.

 Now, let's look where the red line crosses the inner ring. The outer scale (there is presently only one) indicates diameter. Locate the long line marked 0, again. The red line is on top of the first long line which is unmarked but indicates 1, and the next long lines indicate 2, 3, etc.

 So, the estimated required diameter for a 4.0 lbf pulse-jet is 1.0 inch. The claimed thrust for a Dyna-Jet is 4.25 lbf. From its blueprint, the exhaust diameter is 1.25 inch.

[WebPilot]

 the P90:

1. I drew a green line from the origin intersecting the outer ring, inner scale at 19,9 lbf. That is, starting from the 0 line look clockwise for the 10 and 20 marked divisions. There are 10 divisions between them so each denotes 1 lbf. Count 9 and estimate 0,9 of the way to the next small division and you have, 19,9 .
2. Now, look where this green line crosses the inner ring scale which denotes diameter. It crosses 2 + 4 out of 5 divisions to 2,5 or 2,4 inches.

Going to the Team Helmond page for some info and running units on my Linux box to convert the units from MKS to EES.

Code: Select all

$ units
2445 units, 71 prefixes, 33 nonlinear units

You have: 57.5 mm
You want: in
	* 2.2637795
	/ 0.44173913
You have: 85 N
You want: lbf
	* 19.10876
	/ 0.052332019
You have:

 So, I get 2,26 inches and 19,11 lbf from the Team Helmond page and comparing to my wheel's estimation of 2,4 inches and 19,9 lbf ... that's pretty friggin' close!

[WebPilot]

 If you set the line to cross at 19,1 lbf, you will read a value for the diameter of 2,35 in.

 In Linux, I can compute the per cent error based on the Team Helmond value using the BASH shell by typing in a terminal the following.

Code: Select all

$ echo "scale=6;(2.35-2.26)/2.26*100"|bc
3.982300
$

 The "wheel" prediction here is off by a mere +3.98%

[WebPilot]

 You may now be in a position to use this device to answer some questions.

Question #1: The exhaust diameter of an Atom Jet is given as 28 mm. Estimate its thrust.

[Kool]

Hey teacher

28mm=1.102334548 inch

Because I have to look at a picture of A4-format I get first the D² value of 1.102 inch.
(1.102)²=1.215
I drew the line from the origin to the 1.215 value(the D² outer value). The inner scale of the outer ring gives the thrust. Because 1.215 lies approximately in the middle of the D² values of 1 and 1.5 the thrust would be a little under 5 lbf

EDIT

Would it also possible to ad a frequency scale to the figure?
(First I thougt about a fuel consumption scale, but that's depending on many other tings like valve-system and combustion chamer design.)

[WebPilot]

 Smart of you, poech, to use the D² scale; the intervals are further apart and thus more accurate when interpolating.

 Here is a blow-up and I can estimate 4.7 lbf, so we are in agreement, there.

[WebPilot]

Would it also possible to add a frequency scale to the figure?
(First I thought about a fuel consumption scale, but that's depending on many other tings like valve-system and combustion chamer design.)

 Both are dependent upon other variables, and can be done, but each requires another chart.

[WebPilot]

 For the V-1 clone ... follow the blue line in the above pic.

 I drew a line from the center to the outer ring, inner scale, at a value of 487 lbf. We are now at the extreme end section of the scales. Looking at the inner ring, outer scale, the blue line crosses where?

 This may be a little confusing, so pay attention here. The next to the last long line is marked 15. The next one is marked 0. There is a tic marked 15.1 just the left of that line. And the unmarked tic halfway between these two is ... 15.05 .

 So the blue line crosses at ≅ 15.06 in. As a check, one can inspect the outer scale and read 226.9 in². The square root of this value by using a calculator is 15.06 in.

 The V-1 clone used in this example claimed 487 lbf with an exhaust diameter of 15.125 inches. The ring's prediction of 15.06 is in error with this by only -0.430 %.

Code: Select all

$ echo "scale=6;(15.06-15.125)/15.125*100"|bc
-.429700
$