ALTITUDE PREDICTION CHARTS - Ye Olde Rocket Plans

1 TR-10 ALTITUDEPREDICTIONCHARTSMODEL ROCKETTECHNICAL REPORT model Rocket ALTITUDE PREDICTION CHARTS Copyright 1967, 1970, 1971, 1999 Centuri rights 2842TR-10 PREFACEThis report presents a relatively simple method by whichaerodynamic drag effects can accurately be taken intoaccount in the PREDICTION of model Rocket peak altitudes. Withthis data, altitudes can be determined for any Rocket usingany of the Estes motors (including 2 or 3 stage vehicles andcluster-powered rockets). In addition, flight times can be eas-ily found so that optimum engine delay times can be this simple method for calculating aerodynamic drageffects, many interesting experiments and research projectscan be initiated which would have previously been too labori-ous for easy of the easy-to-readgraphs and a few simple arithmetic calculations will enableyou to accurately predict the performances of your modelrockets with different Estes engines.

2 Also, a basic under-standing of the principles of aerodynamics and the aerospacesciences can be obtained by performing the simple dragexperiments suggested at the end of this report. TABLE OF CONTENTSD iscussion of for Using the Graphs ..3 Burnout ALTITUDE and Burnout Velocity Graphs ..6 Coasting Graphs ..24, 25 Sample Problems ..26 - 34 General Equations of model Rocket Motion, Terminology & Equations Converted for model Rocketry 1, The Equations ..35 How to Analyze Two and Three Stage Rockets ..36 References ..36 Appendix II, Suggestions for Drag Experiments ..39 INTRODUCTIONWhen rocketeers get together, the subject for discussion isoften How high do our rockets go?

3 A good solution to this prob-lem has many uses in Rocket design from building the wildestsporter to perfecting the sleekest ALTITUDE report presents the technique of conveniently calculatingall the pertinent parameters you need: burnout ALTITUDE andvelocity, peak ALTITUDE and coast time to peak. The technique isuseful for all types of models including clustered rockets, stagedrockets and example, with the information you calculate you can pickthe optimum weights for the engines you use, the best engine foryour model weight and the correct delay time for your engine andmodel can investigate the performancechange due to variation of parameters such as weight, diameterand drag.

4 Further investigation can tell you if the weight of amodification will be offset by reduced drag or complete parameter trade-off study could be a prize win-ning science fair project and should be part of any high perform-ance Rocket THEORETICAL NO DRAG CONDITIONSVERSUS ACTUAL FLIGHT CONDITIONSIn the June 1964, Rocket Math article (reference I, page36) it was pointed out that typically, drag will reduce thepeak ALTITUDE of a shortened Astron Streak* with a 1/2 A8-4*engine aboard from a theoretical drag free 1935 feet to anactual 710 feet . What this means is simply that merely dueto the effect of air the ALTITUDE has been cut to less than big questions is, Why is this effect so great and what ishappening to the Rocket to cause such a difference?

5 To better understand the effect of the atmosphericforces that retard the forward motion of the Rocket (We aretalking about drag again) let us consider the followingexample. Suppose we have a one inch diameter Rocket (approximate size of BT-50) traveling at 100 Wecan determine the number of air molecules which collidewith our Rocket each second by using Loschmidts number,which is the number of molecules in a cubic centimeter ofgas under standard atmosphere conditions (temperatureof 32 F or 0 C) and pressure of pounds per squareinch, or 76 cm of mercury or newton-seconds /cm).It turns out that during each second of flight time our100 Rocket has to push its way through approxi-mately 400,000,000,000,000,000,000,000 molecules thatlie in its path.

6 (Scientists and engineers usually write outsuch large numbers in the form 4 x 1023, which means 4followed by 23 zeros).Even though molecules are very small, this extremelylarge number of them can add up to a drag force of about1 ounce acting continuously at a speed of 100 drag is proportional to the square of the velocity,**we would then have 4 ounces of drag at 200 and 9ounces of drag on the Rocket at 300 (approximately200 miles per hour).Fortunately, the full effect of these molecules sitting inthe path of our Rocket can be avoided by good streamlin-ing. In this way, most of the molecules are compressed inlayers that tend to flow smoothly around the nose andbody tube as the Rocket passes by them.

7 Relatively fewmolecules are really rammed head-on.*This Rocket or engine is no longer available.**The square of a number is obtained by multiplying thenumber times millions of impacts constitute the effects morecommonly known as aerodynamic drag on a Rocket or,more simply, as just drag . Drag on any object has beenfound to follow this law:D = CDA1/2 V2D is the drag a dimensionless aerodynamic drag coefficient that depends upon the shape and the surface smoothness of the the reference area of the object (for model rockets we use the cross sectional area of the body tube as the reference)(pronounced row ) is the density of the medium through which the object is moving (submarine designers use the density of water in their drag computations, while model rocketeers use the density of air).

8 The density symbol is the Greek letter is the velocity of the objectThe full importance of drag has yet to be realized bymost model rocketeers. It is hoped that through the use ofthe ALTITUDE PREDICTION method presented herein that a morecomplete understanding of its effects will be acquired by DRAG COEFFICIENTThe Aerodynamic Drag Coefficient(CD) is a meas-ure of how easily a given shape moves through (passesby) the molecules of example, a cube traveling with a flat side forwardhas a CDof The following table gives you an idea ofthe importance of streamlining in reducing the aerody-namic drag (flat side forward) (as a marble).47 Clipped teardrop (streamlinedteardrop shape with 1/3 of lengthremoved at trailing edge).

9 1 Streamlined teardrop OF DRAG 2 DRAG FORM FACTORThe product of the aerodynamic drag coefficient (CD)and the frontal area of the object (A) is commonly referredto as the Drag Form Factor (CDA) of the with identical drag form factorwill have identi-cal drag value at any given example, a one-inch cube moving with a flat sideforward would have a drag form factorof inch2( inches). The data below provides additional exam-ples to show the tremendous effect streamlining has onthe drag of a body as reflected in the object s drag provide easy comparisons, a drag form factor(CDA) of inch2has been Area of Object x Drag Coefficient = Drag FormFactor This makes quite clear the great effect streamlining hason reducing drag.

10 A streamlined teardrop with a frontalarea of 21 square inches has the same drag form factoras a 1 inch drag form factorfor most models using standardEstes body tubes may be easily determined by consultingFigure 1, page 6. This graph was derived by calculatingthe cross-sectional area of each body tube and plottingthis as a Pressure Drag Coefficient(CD) of the effective drag is not 100% of the cross-sec-tional area, the drag form factorfor most body tubes atany selected pressure drag coefficientcan be readilyread from the graph or calculated should it occur beyondthe limits of the graph. Aerodynamic Drag of model Rocket , by (Estes Technical Report TR-11), gives a muchmore complete discussion on drag than is contained in thisreport.