Rocket design with elliptical nose cone, by Kemal Payza (variation on an old discontinued Estes design, the Cherokee-D)
The original Cherokee-D used a "secant ogive" nose cone. What is a secant ogive? Go to next page to see!
Estes design, the Cherokee-D)
o next page to see!
1. Purpose
The purpose of this Excel spreadsheet is to calculate and display the profiles of various types of nose cones for
custom production. The results are shown as graphs and also as tables of coordinates for a lathe (radius vs.
2. Scope
The types of basic nose cones shapes included are tangent ogive, secant ogive, parabola, and ellipse. To provide
additional variations on the basic curves, the user can assign a value for a power function that is included as a
variable in each equation. A weighted curve-averaging capability is also included to create shapes that
3. Usage
Enter your desired dimensions in yellow-highlighted cells on the ogive page. You then enter values for shape-
control parameters that spreadsheet or all 4 spreadsheets to design different kinds of nose cones or jigs for your
L Length projecting outside body tube
D Diameter (O.D.) of nose cone at body tube joint
S Length of shoulder (how far the nose cone base projects inside body tube)
T Thickenss of body tube
P Power (exponent) or, in Haack series, the value of parameter used to specify subtype
F X-offset (distance that the ogive or curve is translocated inward)
All these parameters are set on the Ogive page except for P, that you define on each page that you want to use.
Use the same units for all parameters (for example if you enter the diameter in inches, then all entries of length,
thickness, etc. must also be in inches) except for P, which is unitless. Examples of curve shapes obtainable are
shown on each page of the spreadsheet, and on the first page (EQUATIONS) there is a table showing examples
4. Results
The spreadsheet will calculate a result table showing X and Y values in which:
X is the distance along longitudinal axis of nose cone measured from body tube joint (positive values are distance
from the body tube joint towards the tip of the cone, negative values are distance from the joint towards the back
and
Y is the nose cone radius, calculated according to the values entered by the user, at each point X. The Y value is
the radius at which you need to cut your nose cone block with the lathe in order to make the desired shape.
Naturally, the units of X and Y will be the same as you used to define the cone.
Use the OGIVE page to enter the dimensions of the nose cone. All other spreadsheets refer to these values in
5. Display
The spreadsheet will also show you a picture of the nose cone profile. The X-axis automatically adjusts to the
length entered by the user. But for proper scaling of the display, you must adjust the Y-axis to be on same scale
as X (e.g. if X-axis is from -2 to 12 {total of 14 units}, double click on the Y-axis and make it also a total of 14
units, i.e. from -7 to +7). The graphs are set up to be square so that the curves are not distorted. For the display
6. Printing to proper scale
Print the page you are using after making sure you have the same number of units on the X and Y axes (e.g. if X-
axis is from -2 to 12 {total of 14 units}, double click on the Y-axis and make it also a total of 14 units, i.e. from -7
to +7). Then measure the length of the entire nose cone on the printout. Say, for example, you want a 20 cm
cone (L) and 5 cm shoulder (S), so the whole thing should measure 25cm when you print it. But suppose you
masure it and it is only 20 cm. Then you know the right size would be 5/4 of the printout. So you photocopy it
September 25, 1999 revised March 2, 2008 kpayza@sympatico.ca
D Diameter (O.D.) of nose cone at body tube joint Haac
L Length projecting outside body tube P = 1/3
X Distance along nose cone measured from body tube joint
P = 0 gi
Y Radius
P Power (exponent) or parameter used to specify Haack subtype
F X-offset (distance that the ogive or curve is translocated inward)
A Addition of length and X-offset, = L + F Y
S Length of shoulder (inside body tube)
T Thickness of body tube
Ogive family
If 0 0 and 0 and
nd a negative value for X-offset (use ~0.25x L)
d; do not enter a value): 15.09
Related Curves
9.00 Reference
X Y
-3.000
7.00 -3.000
13.000
13.000
5.00
3.00
1.00
radius (Y)
10 12 14
-1.00
-3.00
-5.00
-7.00
-9.00
Questions or comments email Kemal Payza at kpayza@sympatico.ca
Note: If curve looks jagged, this probably due to the screen resolution. Just use the zoom window to enlarge 200%.
Enter value for Power between 0.2 and 1 (true parabola P=0.5) 0.50
Nose cone length & diameter, body tube thickness etc. are set on the Ogive page
X Y neg Y
-3.000 0.000 0.000
-3.000 1.950 -1.950 Parabola and Related Curves
-3.000 1.950 -1.950
0.000 1.950 -1.950
9.00
0.000 2.090 -2.090
0.260 2.069 -2.069
0.520 2.048 -2.048
7.00
0.780 2.026 -2.026
1.040 2.005 -2.005
1.300 1.983 -1.983
5.00
1.560 1.961 -1.961
1.820 1.938 -1.938
2.080 1.916 -1.916
3.00
2.340 1.893 -1.893
2.600 1.869 -1.869
2.860 1.846 -1.846
1.00
radius (Y)
3.120 1.822 -1.822
3.380 1.798 -1.798
3.640 1.773 -1.773 -4 -2 0 2 4 6 8 10 12 14
-1.00
3.900 1.749 -1.749
4.160 1.723 -1.723
4.420 1.698 -1.698
-3.00
4.680 1.672 -1.672
4.940 1.646 -1.646
5.200 1.619 -1.619 -5.00
5.460 1.592 -1.592
5.720 1.564 -1.564
5.980 1.536 -1.536 -7.00
6.240 1.507 -1.507
6.500 1.478 -1.478
6.760 1.448 -1.448 -9.00
7.020 1.418 -1.418
Length (X)
7.280 1.386 -1.386
7.540 1.354 -1.354
7.800 1.322 -1.322
8.060 1.288 -1.288
8.320 1.254 -1.254
8.580 1.219 -1.219
8.840 1.182 -1.182
9.100 1.145 -1.145
9.360 1.106 -1.106
9.620 1.066 -1.066
9.880 1.024 -1.024
10.140 0.980 -0.980
10.400 0.935 -0.935
10.660 0.887 -0.887
10.920 0.836 -0.836
11.180 0.782 -0.782
11.440 0.724 -0.724
11.700 0.661 -0.661
11.830 0.627 -0.627
11.960 0.591 -0.591
12.090 0.553 -0.553
12.220 0.512 -0.512
12.350 0.467 -0.467
12.480 0.418 -0.418
12.610 0.362 -0.362
12.740 0.296 -0.296
12.805 0.256 -0.256
12.870 0.209 -0.209
12.935 0.148 -0.148
13.000 0.000 0.000
Questions or comments email Kemal Payza at kpayza@sympatico.ca
Note: If curve looks jagged, this probably due to the screen resolution. Just use the zoom window to enlarge 200%.
Enter value for Power between 1.5 and 3 (true ellipse P=2) 2.00
Nose cone length & diameter, body tube thickness etc. are set on the Ogive page
X Y neg Y
-3.000 0.000 0.000
-3.000 1.950 -1.950 Ellipse and Related Curves
-3.000 1.950 -1.950
0.000 1.950 -1.950
0.000 2.090 -2.090
0.260 2.090 -2.090
0.520 2.088 -2.088
0.780 2.086 -2.086
1.040 2.083 -2.083
1.300 2.080 -2.080
1.560 2.075 -2.075
1.820 2.069 -2.069
2.080 2.063 -2.063
2.340 2.056 -2.056
2.600 2.048 -2.048
2.860 2.039 -2.039
3.120 2.029 -2.029
3.380 2.018 -2.018
3.640 2.006 -2.006 -4 -2 0 2 4 6 8 10 12
3.900 1.994 -1.994
4.160 1.980 -1.980
4.420 1.965 -1.965
4.680 1.950 -1.950
4.940 1.933 -1.933
5.200 1.916 -1.916
5.460 1.897 -1.897
5.720 1.877 -1.877
5.980 1.856 -1.856
6.240 1.833 -1.833
6.500 1.810 -1.810
6.760 1.785 -1.785
7.020 1.759 -1.759
Length (X)
7.280 1.732 -1.732
7.540 1.703 -1.703
7.800 1.672 -1.672
8.060 1.640 -1.640
8.320 1.606 -1.606
8.580 1.570 -1.570
8.840 1.532 -1.532
9.100 1.493 -1.493
9.360 1.450 -1.450
9.620 1.406 -1.406
9.880 1.358 -1.358
10.140 1.308 -1.308
10.400 1.254 -1.254
10.660 1.196 -1.196
10.920 1.134 -1.134
11.180 1.067 -1.067
11.440 0.993 -0.993
11.700 0.911 -0.911
11.830 0.867 -0.867
11.960 0.819 -0.819
12.090 0.768 -0.768
12.220 0.713 -0.713
12.350 0.653 -0.653
12.480 0.585 -0.585
12.610 0.508 -0.508
12.740 0.416 -0.416
12.805 0.361 -0.361
12.870 0.295 -0.295
12.935 0.209 -0.209
13.000 0.000 0.000
enlarge 200%.
Ogive page
9.00
7.00
5.00
3.00
1.00
radius (Y)
12 14
-1.00
-3.00
-5.00
-7.00
-9.00
Questions or comments email Kemal Payza at kpayza@sympatico.ca
Note: If curve looks jagged, this probably due to the screen resolution. Just use the zoom window to enlarge 200%.
Enter value of parameter P (enter P = 0 for Von Kármán ogive or P = 0.333 for LV-Haack) 0.333
Nose cone length & diameter, body tube thickness etc. are set on the Ogive page
X Y neg Y
-3.000 0.000 0.000
-3.000 1.950 -1.950 Haack series (von Kármán if P = 0)
-3.000 1.950 -1.950
0.000 1.950 -1.950 3.142
9.00
0.000 2.090 -2.090 3.142
0.260 2.087 -2.087 2.858
0.520 2.083 -2.083 2.739
7.00
0.780 2.076 -2.076 2.647
1.040 2.068 -2.068 2.568
1.300 2.059 -2.059 2.498
5.00
1.560 2.049 -2.049 2.434
1.820 2.037 -2.037 2.375
2.080 2.025 -2.025 2.319
3.00
2.340 2.011 -2.011 2.265
2.600 1.996 -1.996 2.214
2.860 1.980 -1.980 2.165
1.00
radius (Y)
3.120 1.962 -1.962 2.118
3.380 1.944 -1.944 2.071
3.640 1.924 -1.924 2.026 -4 -2 0 2 4 6 8 10 12 14
-1.00
3.900 1.903 -1.903 1.982
4.160 1.881 -1.881 1.939
4.420 1.858 -1.858 1.897
-3.00
4.680 1.834 -1.834 1.855
4.940 1.808 -1.808 1.813
5.200 1.781 -1.781 1.772 -5.00
5.460 1.753 -1.753 1.731
5.720 1.723 -1.723 1.691
5.980 1.693 -1.693 1.651 -7.00
6.240 1.660 -1.660 1.611
6.500 1.627 -1.627 1.571
6.760 1.592 -1.592 1.531 -9.00
7.020 1.556 -1.556 1.491
Length (X)
7.280 1.518 -1.518 1.451
7.540 1.479 -1.479 1.410
7.800 1.438 -1.438 1.369
8.060 1.395 -1.395 1.328
8.320 1.351 -1.351 1.287
8.580 1.305 -1.305 1.245
8.840 1.257 -1.257 1.203
9.100 1.208 -1.208 1.159
9.360 1.156 -1.156 1.115
9.620 1.102 -1.102 1.070
9.880 1.046 -1.046 1.024
10.140 0.988 -0.988 0.976
10.400 0.927 -0.927 0.927
10.660 0.863 -0.863 0.876
10.920 0.796 -0.796 0.823
11.180 0.726 -0.726 0.767
11.440 0.651 -0.651 0.707
11.700 0.572 -0.572 0.644
11.830 0.531 -0.531 0.609
11.960 0.488 -0.488 0.574
12.090 0.443 -0.443 0.536
12.220 0.396 -0.396 0.495
12.350 0.346 -0.346 0.451
12.480 0.294 -0.294 0.403
12.610 0.238 -0.238 0.348
12.740 0.176 -0.176 0.284
12.805 0.142 -0.142 0.246
12.870 0.105 -0.105 0.200
12.935 0.063 -0.063 0.142
13.000 0.000 0.000 0.000