Manual cp calculations

Preface: I wrote this article in 1995 before everyone had computers and before CP calculation programs were readily available (you don’t need to call me these days). I was on the ITAP (Interim TAP – before TAP was formalized) and Level 3 projects were coming to me with the attached diagrams calculating CP. You can see the actual formulas used to calculate CP and how to manually calculate CP. If you’re a math junky or just want to see the actual math used read and try the following. Bruce

2/24/95

Center of Pressure Calculations Made EASY

PART 1 - Standard Rockets

By Bruce Lee - Tripoli #1513, L3, Life Member

EASY? YES, it can with this simple fill in the blank plan. Many people have asked me, "How do I calculate Center of Pressure?" First, I tell them about the Handbook of Model Rocketry by Harry Stine. In it is a formidable set of formulas that will allow you to accurately calculate Center of Pressure, or "CP." Or, I tell them, give me a call and I will run it on my computer for you. For those of you who do not have the book, or a computer, or the desire to struggle through the formulas, I have come up with a simple fill in the blank plan. It is so simple that I did a test run with my 10 year old son that tested the calculations with ease. I only had to help him with the single square root calculation (on a calculator). Not only did he do it right, he found a mistake I made on the answer pages (don't you hate it when the kids beat you at your own game). A point to my mistake (2 times 4 is 8, not 2) is, don't even trust yourself, make an extra set of sheets and do the work twice, just to make sure, better safe than sorry!

The formulas used in this article were developed by James S. and Judith A. Barrowman. This is part 1 which will cover a standard rocket without transitions or a boat tail. Part 2 will cover the advanced topics of how to calculate CP on rockets with transitions and/or boat tail. Just in case you didn’t know, a transition is a rocket with multiple body tube diameters and a boat tail is a rocket with transition at the bottom of the rocket by the motor nozzle to reduce drag.

  WHAT TO DO

As can be seen on the next set of pages, there are three blank forms to follow. Now, find a copier (or scanner and print) and copy the blank forms, these will be your working copies.

The first form is your rocket measurements form. As can be seen through out the forms, are the working boxes. Each box contains 3 sections. In the leftmost box is the assigned variable number or nothing. The assigned variable number is used only as an aid to help find the appropriate box. If this part of the box is empty then this represents an intermediate calculation variable. The middle box is the actual variable name which can be found in the full algebraic formulas. If the value is a   

"Z" with a number, this represents an intermediate calculation variable and the number represents the intermediate value that will be used later in another calculation. The right most box is where you will fill in the value of the variable or result of a calculation. 

OK, now back to the measurements page. Get your ruler and tape measure and let's begin measuring. Make each measurement indicated and fill in the appropriate box (right most) corresponding to the indicated measurement with the variable name between the arrows. For example, the box with variable number "1", variable name "LN" (L sub N), which stands for length of nose cone, sits next to "LN" between the two arrows representing the measurement of the length of the nose cone. Measure the nose cone length and fill the empty right most box in "1", "LN". Continue filling in all the boxes on the page. Since there is no transition put a zero in "2", "LT" and "6", "XP". Also, "9", "D" and "10", "DF" and "11", "DR" will all have the same value which is the diameter of the rocket.

CALCULATIONS

NOSE CONE. If your nose cone is conical enter the length of the nose cone on the line that says CONICAL (top of first calculations page) and do the multiplication creating the value for XN. If your nose cone is ogive enter the nose cone length

on the OGIVE line and do the calculation for XN. Only select one of the two and leave the other blank.

FINS. Circle the box with the number of fins your rocket has. Use the "F =" value where it calls for the "14" "F" value in a later calculation and ignore the others.

COEFFICIENT OF FORCE FOR FINS. The actual formula that we will be solving for the coefficient of force for fins comes next preceding the actual calculations. To solve the calculations, find the values you measured and insert them in the appropriate numbered boxes corresponding to the variable to be used in the equation. For example, the first box is looking for the fin semi-span value from your rocket picture with the measurements. Find the box numbered "12" variable name "S" and write the length into box "12" variable name "S" on the first calculations page. Then find the box "13" on the rocket picture with measurements for "R" radius and write the length value into box "13" variable name "R" on the first line and the second line. Add the value of box "12" variable name "S" to box "13" variable name "R" and write the result into the box with variable name "Z1", this is an intermediate variable. Also write this resulting value into the box with variable name "Z1" on the second line. Then on the second line, divide box "13" variable name "R" by the intermediate variable result from the first line "Z1" and write the result into the right most box with the intermediate variable name "Z2". Keep working down the page filling in the variables as you go until you get the final result in box "18" variable name "(CN)F", which is the coefficient of force for fins.

CALCULATIONS - ROUNDING and SQUARE ROOT

I would recommend using a calculator for doing the math. What do you do with all of the digits after the decimal point? Most calculators will fill the display with all of the numbers after the decimal point. Now you can use all of those if you want, but it will make little significant difference to the final result. Two positions after the "." should be sufficient. To do so requires rounding the result to two positions. If the value in the third position is a 5 or greater add 1 to the second position, if it is 4 or less make no changes to the second position. For example: 2.1346 converts to 2.13; 2.1364 converts to 2.14. 

What about that square root thing? A square root is a number times itself, that will equal the original value (the square root of 9 is 3, where 3 times 3 equals 9). Find a calculator with a square root function, the symbol looks like half of a rectangle with an upside down check mark at the front. On the calculator enter the value of "Z11" and hit the square root key and enter the result into "Z12". If that does not work, consult your calculator’s handbook.

PARTIAL CP OF THE FINS

OK, continuing to the second page of the calculations. Start at the top of the page and fill in the boxes top to bottom just like the previous page. Work your way down to the final value, "16" "XF", partial CP of the fins.

SUM THE FORCES

No, don't circle the wagons, it is the next calculation. It adds the force coefficient of the fins and the nose. The value "2" represents the force coefficient of the nose which is the value of "(CN)N". This is the same for both conical and ogive nose cones. The result is the sum of the force coefficients.

CENTER OF PRESSURE - FINAL CALCULATION

You are almost done. This calculation is the sum of the products of the force coefficient and the partial CP of each part divided by the total rocket force coefficient. The final value, "Z29", is the location of the Center of Pressure from the tip of the nose cone. Get the tape measure out again. Starting at the tip of the nose cone measure down the rocket the distance represented by "Z29". Do not follow the contour of the nose. Mark this point for future reference.

IS IT SAFE?

Good question. First go back to your blank forms and start over from scratch. Re-measure and re-calculate everything, don't just copy the answers from the first attempt. Is the answer the same? If yes, go on, if no, do the forms a third time or find your mistake by comparing the first attempt to the second attempt. This is serious stuff; you really want to be right. No one wants a high power rocket spinning around uncontrollably nearby!

Now that you know where the Center of Pressure is, you can determine if your rocket is safe. Assemble and load your rocket with its motor and parachute and anything else it will fly with. Now find your Center of Gravity (CG). This is easy, no calculations. Find the point on the rocket where it balances and that is the Center of Gravity. An easy way to do this is to get a rope and tie it around your rocket near the center for a starting point. Pick up the rocket by the rope, one of the ends will be pointing toward the ground. Move the rope towards the end of the rocket pointing towards the ground. Keep adjusting the rope until neither end of the rocket points down and is balanced on the rope when picked up. Mark the point where the rope is on your rocket, this is the Center of Gravity. 

First safety check. Is the Center of Pressure closer to the tail of the rocket than the Center of Gravity? If the answer is yes, then you are ok. If the answer is no (CG is closer to the fins), you have a seriously unstable rocket. You will need to add weight to the payload section or nose cone to move the Center of Gravity forward. 

Second safety check. Now measure the distance between the Center of Pressure and the Center of Gravity. The minimum safe distance between CP and CG is equivalent to one body tube diameter (4” diameter body tube equal 4” between CP and CP), or in this example, box "9" variable "D". If this value is less than one body tube diameter, you must add weight to the forward area of the rocket to bring Center of Gravity forward towards the nose until you have at least one body tube diameter between them.

OK, that's it. You did it. Congratulations! You now know where the CP and CG are and you also know if your rocket is safe.