[American Institute of Aeronautics and Astronautics 47th AIAA Aerospace Sciences Meeting including...

1

American Institute of Aeronautics and Astronautics This material has been approved for public release by U.S. Army AMRDEC and Dynetics, Inc.

Recent Improvements for the 8/08 Release of Missile Datcom

Josh B. Doyle1

Dynetics, Inc., Huntsville, AL, 35806

and

Christopher C. Rosema2, Mark L. Underwood

3 and Lamar M. Auman

4

US Army AMRDEC, Redstone Arsenal, AL 35898

Missile Datcom is an industry-standard tool used for predicting the aerodynamic stability

and control performance of conventional missile configurations. In August 2008, the US Air

Force Research Laboratory (AFRL) and the US Army Aviation and Missile Research,

Development, and Engineering Center (AMRDEC) released the 8/08 version of the Missile

Datcom code. Among the major changes introduced were: 1) significant revisions to the

axial force prediction methodology for bodies with blunted, truncated, and low fineness ratio

noses and 2) an additional capability that permits the user to specify angular orientations for

body protuberances, thereby allowing the calculation of incremental pitching and/or yawing

moments resulting from protuberance drag. This paper documents the process utilized in

developing, implementing, and validating the updated methods in the 8/08 release of Missile

Datcom, and includes comparisons with experimental and computational fluid dynamics

data.

Nomenclature

A = oblique cross sectional area projection

CAF = forebody axial force coefficient

CApres = pressure contribution to forebody axial force coefficient

CAfric = skin friction contribution to forebody axial force coefficient

CAU = uncorrected axial force coefficient

CM protub = pitching moment coefficient increment due to protuberance

CN = normal force coefficient

Cn protub = yawing moment coefficient increment due to protuberance

Lref = reference length (maximum body diameter for this paper)

M = Mach number

Sref = reference area (maximum body cross sectional area for this paper)

Yprotub = horizontal distance from moment reference point to protuberance centroid

Zprotub = vertical distance from moment reference point to protuberance centroid

α = angle of attack

η = conical nose half-angle

μ = Mach angle

I. Introduction

HE US Army Aviation and Missile Research, Development and Engineering Center (AMRDEC) and the US

Air Force Research Laboratory jointly agreed to the continual development of Missile Datcom in 2004. The

goal of this effort is to: 1) improve the accuracy of the code within the existing design space and 2) expand the

design space to include methods for predicting the aerodynamics of unconventional missile configurations.

1 Aerospace Engineer, AIAA Member.

2 Aerospace Engineer, AIAA Member.

3 Senior Aerospace Engineer, AIAA Senior Member.

4 Branch Chief, Aerodynamics Technology Function, Aviation and Missile RDEC, AIAA Senior Member.

T

47th AIAA Aerospace Sciences Meeting Including The New Horizons Forum and Aerospace Exposition5 - 8 January 2009, Orlando, Florida

AIAA 2009-907

This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States.

2

American Institute of Aeronautics and Astronautics

Missile Datcom is an industry standard aerodynamic prediction tool used commonly used for preliminary missile

design due to its relatively simple inputs and short run time. It utilizes both empirical and theoretical methods to

obtain aerodynamic predictions from low subsonic speeds to hypersonic speeds. The code was originally released in

August 1984, and since that time, numerous versions containing improvements and additions have been released

with the most recent being the 7/07 and 8/08 versions. This paper documents two of the major improvements and

additions made to Missile Datcom from the 7/07 release to the 8/08 release: significant revision of the axial force

prediction methodology for bodies with blunted, truncated, and low fineness ratio noses, and the additional

capability permitting the user to specify angular orientations for body protuberances.

In an attempt to identify discontinuities in aerodynamic predictions generated by the 7/07 version of Missile

Datcom, tools were developed to execute the code over a range of varying geometric inputs such as nose shape, nose

length, body diameter, etc. Results were then collected and plotted as functions of Mach number, angle of attack,

and the variable geometry parameters. One of these surveys uncovered large discontinuities in CAF predictions for

bodies with short conical noses and/or highly truncated noses. Comparisons to experimental and CFD data indicated

that these predictions were very inaccurate in many cases. An effort was subsequently undertaken to discern the

source of these discontinuities and to develop and implement methods to resolve the issues in order to improve

prediction accuracy. As a result of this effort, modifications were made to body CAF prediction methodologies in the

subsonic, transonic, and supersonic flight regimes. Truncated and low fineness ratio noses were the primary areas of

interest. Section II documents the results of this effort, including a description of the observed data discontinuities, a

discussion of key method changes, and comparisons of the revised predictions to experimental and CFD data. In

general, the resulting code modifications eliminated the discontinuous data trends and improved prediction accuracy.

In addition to method changes introduced in axial force calculations, the ability to specify protuberance angular

orientation was also added to Missile Datcom 8/08 and is discussed in Section III. With a specified angular

orientation, pitching and yawing moment increments are now calculated based on the axial force of the protuberance

and its distance from the moment reference point.

II. Forebody Axial Force Coefficient Modifications

The computation of body axial force in Missile Datcom is a multi-step process. Tables 1 and 2 list the

subroutines involve in the calculation and Fig. 1 shows a flowchart to the process used in the 7/07 version of the

code. The yellow boxes indicate places where changes were made for the 8/08 version of Missile Datcom. The path

of the flow chart is generally determined by freestream Mach number with two exceptions. First, for M≤1.2, a

critical Mach number is calculated to determine if the body has reached the point of drag divergence in the transonic

region. This calculation is dependent on nose bluntness. Second, for supersonic Mach numbers, hybrid theory will

sometimes fail depending on the combination of Mach number and body geometry, and if this occurs, SOSE theory

is utilized.

Table 1. Subsonic/Transonic Body Axial Force Coefficient Subroutines

BODYCA top level routine for subsonic/transonic body alone CA

MDIV computes drag divergence Mach number

CDPROT computes protuberance CA increment

CAFRIC computes skin friction based on wetted area

BDCAPR computes subsonic zero angle of attack form drag

CDPRES computes transonic CApres

BDCDVR computes subsonic/transonic boattail CApres

BDCAWF computes subsonic/transonic flare CApres

BDCAB computes CABase

Table 2. Supersonic/Hypersonic Body Axial Force Coefficient Subroutines

SUPBOD top-level routine for computing CA, CN, and CM for supersonic speeds

CAFRIC computes skin friction based on wetted area

CDPROT computes protuberance drag

SUPPOT routine for calling HYPERS, HYBRID, and SOSE

HYPERS computes hypersonic CA, CN, and CM

HYBRID computes CA, CN, and CM using Van Dyke hybrid theory

SOSE computes CA, CN, and CM using Second-Order Shock Expansion (SOSE) theory

3


Figure 1. Missile Datcom 7/07 Body CAF Calculation Flowchart

In order to identify discontinuities in the aerodynamic predictions generated by the 7/07 version of Missile

Datcom, a tool was developed to execute parametric sweeps of specific geometric inputs (i.e. a “geometry sweep”)

such as nose shape, nose length, body diameter, etc. Predictions generated by the code were collected and plotted

against Mach number, angle of attack, and the variable geometry parameters. One such survey involved a simple

cylindrical body with a conical nose; no finsets or protuberances were present. A sweep of nose cone half-angle was

performed while keeping total body length and diameter constant. Figure 2 shows a sketch of the baseline body

geometry with three different nose cone half-angles and Table 3 lists the basic dimensions. A total of 19 different

conical nose half-angles were evaluated, ranging from 10 to 89.9 deg.

Body Alone

CAF Calculation

Compute Mcrit

M ≤ 1.2

If SOSE

control card

is used

Compute Skin

Friction Coefficient

M ≤ Mcrit M > Mcrit

Compute Subsonic

Pressure Drag(Form Drag Method)

Find CApres and

dCApres/dM at Mcrit

(Form Drag Method)

Find CApres and

dCApres/dM at M=1.2(Supersonic Area Rule)

Curve fit CApres vs. Mach

with cubic polynomial to obtain CApres at M

Compute Skin


Compute Skin


M > 1.2

Attempt Van Dyke’s

Hybrid Method to solve for CApres

Use Second-Order Shock

Expansion Theory (SOSE) to solve for CApres

If Hybrid

Method Fails

Table 3. Conical Nose Study Basic Body Dimensions

Total Length 40.0 in

Body Diameter 5.0 in

Lref 5.0 in

Sref 19.635 in2

Nose Half-Angle 10 to 89.9 deg

4


Figure 2: Baseline Body Geometry for Conical Nose Study

Figure 3. CAF v. Mach for Varying Conical Nose Half-Angles (α = 0 deg.), Missile Datcom 7/07 Results

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0-10

-5

0

5

10

15

20

25

30

Mach Number

Fore

body A

xia

l F

orc

e C

oeff

icie

nt,

CA

F

10.0 deg.

35.0 deg.

45.0 deg.

50.0 deg.

55.0 deg.

60.0 deg.

74.0 deg.

86.0 deg.

Cone Half-Angle = 50 deg.

Cone Half-Angle = 55 deg.

Half-Angle

5


Figure 4. CAF v. Nose Cone Half-Angle, Missile Datcom 7/07 Results

Figure 3 presents CAF results generated by the 7/07 version of Missile Datcom as a function of Mach number for

each of the nose cone half-angles. As illustrated, CAF values in the transonic Mach regime range from -10 to +30,

and are clearly erroneous. Note also the discontinuity at Mach=1.2, which is the result of a calculation method

change. Figure 4 shows these same data as a function of nose cone half-angle for Mach numbers of 0.2, 0.8, 1.2,

and 2.0. The predictions at Mach=2.0 appear reasonable while the sharp discontinuities exist at all other Mach

numbers. Again, note the unreasonable CAF values that approach -10 and +30 in the transonic range.

References 1, 2, and 3 contain experimental data for a flat-faced cylindrical body similar to the one described in

Table 3. Figure 5 shows a plot of CAF and CAU as a function of Mach number from this data set. According to the

data in References 1, 2, and 3, a fully truncated nose (i.e. a 90-deg nose cone half-angle) with a cylindrical body

should have a CAF value ranging from approximately 0.78 at subsonic Mach numbers to approximately 1.55 at

Mach=3.0. These results further confirm the inaccuracy of the predictions generated by the 7/07 version of Missile

Datcom. The subsequent sections of this paper describe the process used to identify the root cause of the erroneous

predictions and to develop and implement solutions to improve prediction accuracy.

10 20 30 40 50 60 70 80 90-0.5

0.0

0.5

1.0

1.5

2.0

Nose Cone Half-Angle (deg)

Fore

body A

xia

l F

orc

e C

oeff

icie

nt,

CA

F

Mach = 0.2

= 0

= 4

= 8

10 20 30 40 50 60 70 80 90-10

-5

0

5

10

15

20

25

30


Fore

body A

xia

l F

orc

e C

oeff

icie

nt,

CA

F

Mach = 0.8

= 0

= 4

= 8

10 20 30 40 50 60 70 80 900

5

10

15

20

25


Fore

body A

xia

l F

orc

e C

oeff

icie

nt,

CA

F

Mach = 1.2

= 0

= 4

= 8

10 20 30 40 50 60 70 80 900.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8


Fore

body A

xia

l F

orc

e C

oeff

icie

nt,

CA

F

Mach = 2.0

= 0

= 4

= 8

6


Figure 5. Axial Force Coefficient for a Generic Body with a Fully Truncated Nose

A. Transonic Axial Force Corrections

In the 7/07 version of Missile Datcom, the prediction of CAF in the transonic region involves fitting a cubic

polynomial curve to computed values of CApres (the pressure contribution to forebody axial force coefficient). This

curve fit is generated at the critical Mach number (Mcrit) and at Mach=1.2 and requires a calculation of the

derivatives of CApres with Mach number at those points. Derivatives are approximated by perturbing Mach number

by 0.01 for Mcrit and by 0.1 at Mach=1.2, as shown in Equation (1) and (2).

01.0

01.0critcritcrit MM

presA

MM

presA

M

presA CC

M

C (1)

1.0

2.13.12.1 M

presA

M

presA

M

presA CC

M

C (2)

In Missile Datcom versions 7/07 and prior, CApres at Mach=1.2 and Mach=1.3 was evaluated using the supersonic

area rule, numerically integrated over the body, as shown in Equation (3). See Reference 4 for a complete derivation

of this method. Note that L is the length of the body while x1 and x2 are integration variables representing axial

stations. At first glance, CApres appears to be a function of cross sectional area alone, but here, A is the projection of

an oblique cross-sectional area onto a plane perpendicular to the body centerline. The corresponding oblique angle is

the Mach angle given in Equation (4). Thus, CApres becomes a function of cross sectional area and Mach number.

210 0

212

1

2

2

1

2

ln2

1dxdxxx

dx

Ad

dx

Ad

SC

L L

ref

presA (3)

)/1(sin 1 M (4)

In Missile Datcom 7/07, this approach is only used in the calculation of the upper end of the transonic CApres

curve fit (Mach=1.2 and Mach=1.3) and drag prediction on inlets. Consequently, only CApres values in the transonic

range (M=Mcrit to M=1.2) contained the effects of the supersonic area rule. Mach>1.2 CApres values were found by

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Ax

al F

orc

e C

oe

ffic

ien

t, C

A

Mach

CAU - Hoerner (Ref. 1)

CAF - Hoerner (Ref. 1)

CAU - BLUFBD Database (Ref. 2)

CAF - BLUFBD Database (Ref. 2)

CAU - FFA-TN-1984-04 (Ref. 3)

7


either hybrid or SOSE theory. The erratic behavior occurring for 50 and 55 deg conical nose half-angles (see Fig. 3)

is a direct result of numerically integrating Equation (3) with oblique angle cross sections. The Mach angles at

M=1.2 and M=1.3 are 56.44 and 50.28 deg, respectively. When the nose cone angle approaches one of these angles,

the two CApres terms in Equation (2) are far apart and produce a very large positive or negative slope for the cubic

curve fit, resulting in the erroneously high magnitudes for CAF shown in Fig. 3 and 4. In Missile Datcom 8/08, the

supersonic area rule method of Equation (3) was replaced with a combination of Van Dyke hybrid theory and SOSE

theory, which is described in detail in Section II.B. This results in two significant improvements. First, Datcom can

now more accurately predict axial force for a greater range of nose shapes. Second, the use of Van Dyke hybrid

theory and SOSE at the supersonic end of the cubic eliminates the discontinuity at Mach=1.2 caused by the change

in prediction methods.

Figure 6. Conical Nose CAF Using Revised CApres Calculation (α = 0 deg)

Figure 6 shows CAF as a function of Mach number for conical noses using the revised CApres calculation. As

shown, trends with increasing conical nose angle are captured, discontinuities at Mach=1.2 are eliminated, and

magnitudes of CAF are within reason on the upper end of the transonic region. However, CAF values appear to be too

small in the subsonic region as the geometry approaches a flat faced cylinder. A resolution to this issue is described

in Section II.C.

While the preceding analysis has focused on conical nose shapes, other nose types had similar problems with the

supersonic area rule used in Missile Datcom 7/07. Figure 8 shows CAF predictions for various length ogive noses

generated by Missile Datcom version 7/07 and 8/08. Values on the transonic side of Mach 1.2 were reasonable with

the supersonic area rule due to a previous correction described in Reference 5. Although this correction produced

accurate CAF values for Mach<1.2, the discontinuity at Mach=1.2 was still present. In the case of ogive noses, the

replacement of the supersonic area rule with the Van Dyke-SOSE combination ensured continuity across Mach

number and geometric trend, while sacrificing a small amount of accuracy just below Mach=1.2. The loss of

accuracy is illustrated in the transonic region of Fig. 9.

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.00.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

Mach Number

Fore

body A

xia

l F

orc

e C

oeff

icie

nt,

CA

F

10.0 deg

20.0 deg

30.0 deg

40.0 deg

50.0 deg

70.0 deg

90.0 deg

Nose Half-Angle

8


Figure 7. Baseline Body Geometry for Conical Nose Study

Figure 8. Ogive Nose CAF v. Mach, Effect of Revised CApres Method (α=0 only)

Figure 9. Comparison of Experimental CAF for a Hemispherical Nose

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.00

0.2

0.4

0.6

0.8

1

1.2

1.4

Mach Number

Fore

body A

xia

l F

orc

e C

oeff

icie

nt,

CA

F

Datcom 7/07

0.50 calibers

0.70 calibers

0.90 calibers

1.10 calibers

1.40 calibers

1.70 calibers

2.00 calibers

4.00 calibers

Nose Length

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.00.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Mach Number

Fore

body A

xia

l F

orc

e C

oeff

icie

nt,

CA

F

Datcom 8/08

0.50 calibers

0.70 calibers

0.90 calibers

1.10 calibers

1.40 calibers

1.70 calibers

2.00 calibers

4.00 calibers

Nose Length

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Fore

bo

dy

Axi

al F

orc

e C

oe

ffic

ien

t, C

AF

Mach Number

Datcom 7/07 (6 caliber body)

Datcom 8/08 (6 caliber body)

Experimental (Ref. 8 - Mach Sweep)

Experimental (Ref. 8 - Alpha Sweep)

Experimental (Ref. 2 - 5 cal body)

Experimental (Ref. 2 - 7 cal body)

9


B. Supersonic Axial Force Corrections

Two discontinuities exist in Missile Datcom 7/07 CAF predictions in the supersonic region. The first was resolved

with the replacement of the supersonic area rule as described in the previous section. The second discontinuity

occurs when hybrid theory fails and the code switches to using SOSE theory. Van Dyke hybrid theory, as

implemented in Datcom, will fail when the local slope on any point of the nose exceeds the freestream Mach angle

given by Equation (4). Figure 10 illustrates this transition for various nose cone half-angles for the body from Table

3. For higher fineness ratio noses (small nose cone half-angles), there is not a large difference between the two

prediction methods. As the fineness ratio of the nose decreases (nose cone half-angle increases), the CAF variance

between methods grows until the limitations of hybrid theory are reached and Datcom switches to SOSE. This

transition can result in discontinuous CAF predictions.

Figure 10. Effect of Hybrid to SOSE Transition on CAF for Conical Noses (Datcom 7/07, α=0 deg)

To address this issue, a smoothing subroutine was written to transition from hybrid to SOSE as Mach number

increases. This subroutine is based on studies performed in Reference 6 that designate the optimal conditions for the

use of hybrid and SOSE theory. Figure 11 from Reference 6 shows the recommended usage ranges of hybrid and

SOSE theories as a function of Mach number and nose fineness ratio. The upper line is the recommended limit to

SOSE application. The lower line represents the theoretical limit to Van Dyke hybrid theory, which is dependent on

the maximum slope on any point of the nose (in nearly all cases, this occurs at the nose tip). The lower line is

different for each nose type.

The smoothing subroutine works by finding the position of the defined nose geometry on Figure 11. If that

position falls in the “overlap” region, Missile Datcom will execute both hybrid and SOSE methods and then use a

weighted interpolation scheme between the two. The weighting variable, HYSOFR, is dependent on the position of

the nose geometry on Fig. 11. A HYSOFR value of 1 corresponds to 100% SOSE and a value of 0 corresponds to

100% hybrid theory. A HYSOFR value of 0.5 would cause the code to simply average the SOSE and hybrid values.

1.2 1.25 1.3 1.35 1.4 1.45 1.5 1.55 1.60.7

0.9

1.1

1.3

1.5

1.7

Mach Number

Fore

body A

xia

l F

orc

e C

oeff

icie

nt,

CA

F

29.05 deg

35.54 deg

41.76 deg

46.17 deg

51.34 deg

57.38 deg

Hybrid theory limit

(Datcom switches

to SOSE theory)SOSE theory used for all

Mach numbers shown

Hybrid Theory used for all Mach numbers shown

Nose Half-Angle

10


Figure 12 shows an example of how the method employed in Missile Datcom 8/08 calculates the HYSOFR

variable for an ogive nose. At the given Mach number, Missile Datcom will interpolate based on a vertical line

between the upper (SOSE) and lower (hybrid) limits to determine whether hybrid theory, SOSE theory, or a

combination of the two should be used. Figure 13 shows predictions from hybrid, SOSE, and the combined method

used in Datcom 8/08 for various nose shapes. While typical low-drag noses (i.e. high fineness ratio) will see little

change from the blended hybrid-SOSE method, it is necessary for continuity of CAF predictions for low fineness

ratio noses.

Figure 13. Combined Hybrid-SOSE CAF Prediction for Conical Noses (α=0 deg)

1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.601.00

1.05

1.10

1.15

1.20

1.25

1.30

1.35

1.40

Mach Number

Fore

body A

xia

l F

orc

e C

oeff

icie

nt,

CA

F

37.9987 deg Hybrid

41.7603 deg Hybrid

46.1691 deg Hybrid

37.9987 deg SOSE

41.7603 deg SOSE

46.1691 deg SOSE

37.9987 deg Combined



Nose Half-Angle

Figure 11. Recommended SOSE and Figure 12. SOSE and Hybrid Regions for Ogive

Hybrid Application Regions (Ref. 6) Noses Determined by HYSOSE, Datcom 8/08

0

2

4

6

8

1 2 3 4 5

Mach NumberN

os

e F

ine

ne

ss

Ra

tio

SOSE U

pper L

imit

Hybrid Lower L

imit (Ogive nose)

100%

Hybrid

100%

SOSE

HYSOFR = 0.00

HYSOFR = 0.67

HYSOFR = 1.00

HYSOFR = 0.33

HYSOFR = 0.50

0

2

4

6

8

1 2 3 4 5

Mach NumberN

os

e F

ine

ne

ss

Ra

tio

SOSE U

pper L

imit

Hybrid Lower L

imit (Ogive nose)

100%

Hybrid

100%

SOSE

HYSOFR = 0.00

HYSOFR = 0.67

HYSOFR = 1.00

HYSOFR = 0.33

HYSOFR = 0.50

11


C. Subsonic Axial Force Corrections for Low Fineness Ratio Noses

Missile Datcom version 7/07 computes subsonic pressure drag using the form drag method (described in

Reference 7), which is a function of body fineness ratio and skin friction. For noses with little to no flow separation,

this method provides sufficient results. However, for cases with moderate to severe flow separation on the nose,

such as truncated noses and low fineness ratio noses, the form drag method greatly under predicts pressure drag.

Experimental data from Reference 1 suggest that the CAF for a fully truncated nose (i.e. nose fineness ratio of zero)

on a cylindrical body in the subsonic regime has a value of approximately 0.86 (see Fig. 5). In the 7/07 version of

Missile Datcom, the predicted CAF value for this configuration is approximately 0.1.

To correct this discrepancy, it was determined that a curve fit of CAF with nose fineness ratio could be used to

blend the Missile Datcom computed form drag to the experimental value for the fully truncated nose pressure drag.

A CFD study using the NASA flow solver, OVERFLOW (version 2.1g), was conducted to aid in developing this

curve fit. OVERFLOW is a Reynolds-averaged Navier-Stokes code that uses structured overset grids. Full-body,

three-dimensional cases were run at sea-level Reynolds numbers. A viscous adiabatic wall boundary condition was

applied on the body with a freestream/characteristic condition set at the farfield boundaries. A y+ of approximately

one was used for initial grid spacing off the wall. All viscous terms were included in the simulations, which used

the Spalart-Allmaras one-equation turbulence model. The second-order HLLC upwind scheme was chosen as the

inviscid flux algorithm while the ARC3D Beam-Warming with Steger-Warming flux split jacobians algorithm was

selected for the implicit solver. The farfield boundary extended 40 characteristic body lengths away from the body

in all directions. The resulting grid contained 1.75 million points. Cases were run at Mach numbers of 0.2, 0.5, 0.8,

and 1.2 and nose fineness ratios of 2.0, 1.0, 0.75, 0.5, 0.25, and 0 (fully truncated). Variance of axial force

coefficient was less 1% for the last 1000 iterations on all cases. Figure 14 shows an example convergence history for

the Mach 0.5, one caliber nose case.

Figure 14. CFD Convergence History for 1-Caliber Conical Nose (M = 0.5, α = 0)

Figure 15 shows the results of the CFD simulations. The following process was used to get the data into a form

suitable for the polynomial curve fit to be implemented in Datcom. The data were first normalized at each Mach

number by the fully truncated nose CApres to determine CApres for each cone angle as a fraction of fully truncated nose

CApres. Next, the data were rescaled (based on the lowest axial force value) to range from zero to one. This value is

depicted in Fig. 16 and represents a newly defined conical nose factor, which is utilized as shown in Equation (5) in

the CApres calculation. Note that for nose fineness ratios greater than 1.5, the truncated CApres factor is set to zero as

the form drag is sufficient by itself.

12


formAformAtrunAprespresA CCCFactorNoseConicalC )(* (5)

AfrictrunApres CC 86.0 (6)

Figure 15. CAF vs. Mach, CFD Results for Low Fineness Ratio Noses (α=0 deg)

Figure 16. Short Conical Nose CApres Curve Fit

CFD Axial Force Predictions

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Mach

CA

F0

truncated nose

0.25 cal. nose

0.50 cal. nose

0.75 cal. nose

1.0 cal. nose

2.0 cal. nose

y = -0.22902x3 + 1.1354x2 - 1.8549x + 1.0

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.00 0.50 1.00 1.50 2.00 2.50

Co

nic

al N

os

e C

Ap

res

Fa

cto

r

Nose Fineness Ratio

Short Conical Nose CApres Curve Fit

CFD, M=0.2

CFD, M=0.5

CFD, M=0.8

CFD, M=1.2

Polynomial Curve Fit

13


Figure 17 shows the effect of this change (compare to Fig. 6) on the subsonic CAF for the conical nose case from

Table 3. As the conical nose half-angle approaches 90 deg (fully truncated), the data approach the known value for a

flat-faced cylinder. All intermediate angles follow the expected trend of drag rise with increasing conical half-angle.

Figure 17. Conical Nose CAF vs. Mach, Effect of Subsonic Corrections (α=0 deg)

A comparison with experimental data for a cylindrical body is shown in Fig. 19. The test configuration is shown

in Fig. 18 and consists of a cylindrical body with a 60 deg half-angle conical nose (Ref. 8). The test was conducted

at Mach=0.25 and a Reynolds number of 1.6x106/ft. Reference area was the max body cross-sectional area, 3.976

in2. As illustrated, the revised method used in Missile Datcom 8/08 shows considerable improvement in forebody

axial force prediction.

Figure 18. Experimental 60-deg Conical Nose Configuration

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.00.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

Mach Number

Fore

body A

xia

l F

orc

e C

oeff

icie

nt,

CA

F

10.0 deg.

20.0 deg.

30.0 deg.

40.0 deg.

50.0 deg.

70.0 deg.

90.0 deg.

Nose Half-Angle

14


Figure 19. Wind Tunnel Test Comparison for 60-deg Conical Nose Half-Angle, M=0.25

D. Subsonic Axial Force Corrections for Truncated Noses

For partially truncated noses in subsonic flow, a similar approach was taken to revise axial force predictions as

the one described for low fineness ratio noses. For subsonic CAF, Datcom 7/07 used an interpolation between form

drag and fully truncated drag based on truncation ratio (truncation ratio=truncated diameter/nose base diameter). In

an attempt to improve upon this method, CFD simulations were run for various truncation ratios of 14-deg conical

noses (shown in Fig. 20). The truncated nose simulations were run with the same flow solver, scheme, turbulence

model, and convergence criteria as the conical nose simulations from Section II.C. Half-bodies with inviscid walls

were used rather than full bodies. The use of a wall function decreased total grid size as y+ values varied between 30

and 50. The subsonic farfield boundary was 20 to 25 characteristic body lengths from the body, while supersonic

simulations (not used for this particular curve fit) had farfield boundaries between three and five characteristic body

lengths.

Results are presented in Fig. 21. As shown, small changes in geometry can produce large changes in axial force,

primarily for high truncation ratios (between 0.7 and 1.0). Figure 22 shows the curve fit utilized in Datcom 8/08,

which was derived using a similar approach as that described for low fineness ratio noses, Equation (5) is then

utilized for the CApres calculation.

Figure 20. Geometry from Partially Truncated CFD Simulations

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 2 4 6 8 10 12

CA

F

Angle of Attack (deg)

WT Test Data

8/08 Datcom

7/07 Datcom

15


Figure 21. CAF vs. Mach, CFD Results for Truncated Noses (α=0 deg)

Figure 22. Truncated Nose CApres Curve Fit

Figure 24 compares Datcom 7/07, Datcom 8/08, and experimental CAF for a chamfered nose configuration

shown in Fig. 23 (Ref. 8). The configuration consists of a partially truncated conical nose attached to a cylindrical

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0.2 0.4 0.6 0.8 1.0 1.2 1.4

Fo

reb

od

y A

xia

l F

orc

e C

oeff

icie

nt,

CA

F

Mach Number

Truncation Ratio = 0.0







0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 0.2 0.4 0.6 0.8 1.0

Tru

ncate

d C

Ap

res

Facto

r

Truncation Ratio

M = 0.3

M = 0.6

M = 0.9

Polynomial Fit

Datcom 7/07 Linear Interpolation

16


body with a length of 8.1 calibers. The configuration was tested from Mach 0.6 to 1.6 with Reynolds numbers

ranging from 3.9x106/ft to 8.0x10

6/ft. Reference area was the max body cross-sectional area, 11.04 in

2. The

corresponding truncation ratio for the chamfered nose is 0.905, and the nose falls into a region of great sensitivity in

CAF. The Datcom 8/08 prediction is slightly more accurate than Datcom 7/07 in the low subsonic range, and the

Datcom 8/08 CAF prediction is continuous across Mach number due to the removal of the supersonic area rule, as

described in Section II.A.

Figure 23. Geometry for Chamfered Nose Configuration

Figure 24. Wind Tunnel Test Comparison for Chamfered Nose (α=0 deg)

III. Protuberance Angular Orientation

The second major change incorporated in the 8/08 release of Missile Datcom is related to protuberance

modeling. Missile Datcom provides the user with the ability to model six different types of body protuberances:

vertical cylinders, horizontal cylinders, lugs, shoes, blocks, and fairings. Protuberances can be placed at up to 20

different axial stations along the body with an unlimited number of identical protuberances at each station. Missile

Datcom computes the incremental CA for a given protuberance set by multiplying the CA of an individual

protuberance by the total number of protuberances in that set. In the 7/07 version of the code, the only effect of

protuberances is a CA increment. With the 8/08 release, an attempt was made to expand the effects of protuberances

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

CA

F

Mach Number

Datcom 7/07

Datcom 8/08

WT Test Data (Mach Sweep)

WT Test Data (alpha sweep data)

17


to include pitching and/or yawing moments resulting from the axial load acting on the protuberances. This was

accomplished through the inclusion of an angular orientation option in the protuberance definition input.

A protuberance angular orientation option was added to the Missile Datcom user input file to allow the user to

define the orientation angle (from 0 to 360 deg) for each individual protuberance. This information allows Datcom

to calculate a moment arm to be used in conjunction with the existing protuberance axial force to compute an

incremental pitching and/or yawing moment. No rolling moment is produced because the force acts in the axial

direction. Note that the protuberance moment arm is measured from the configuration MRP to the protuberance

centroid (see Fig. 25).

In reality, it is possible for protuberances to also have an impact on normal force, side force, and rolling moment

at high total angles of attack. At high total angles of attack, any contribution of protuberances to normal force, side

force, and rolling moment would typically be negligible in comparison to the total configuration forces and

moments. In addition, the semi-empirical prediction methods employed by Missile Datcom at high angles of attack

are generally not extremely accurate, and any protuberance effects would likely be within the prediction uncertainty

at those conditions. Thus, increments due to protuberance normal force, side force, and the corresponding moments

are neglected. Attempts to quantify these effects may be included in future versions of the Missile Datcom code.

Other second-order effects such as body shielding and vortex interactions are also neglected in protuberance

calculations.

Figure 27 shows a sample protuberance input for a generic missile body with six total protuberances at three

different axial stations. PHIPRO is the input variable for angular orientation of each protuberance and is ordered by

protuberance set. The first two PHIPRO values correspond to the two protuberances in the first set, the third value

corresponds to the lone protuberance in the second set, and last three values correspond to the three protuberances in

the third set. Angles are measured positive clockwise when viewed from the rear of the missile (see Fig. 26). Figure

28 shows a sketch of the protuberances defined in Fig. 27.

Figure 25. Protuberance Geometric Moment Arm Figure 26: PHIPRO Definition

18


$PROTUB

NPROT = 3., * number of protuberance sets

PTYPE = FAIRING,VCYL,FAIRING, * protuberance type

XPROT = 50.00,60.0,70.0, * axial station for each set

NLOC = 2.,1.,3., * number of protuberances in each set

PHIPRO = 0.,180.,270.,60.,180.,300., * angular orientation of protuberances

LPROT = 2.00,3.0,2.0, * length of protuberances by set

WPROT = 2.00,5.0,2.0, * width of protuberances by set

HPROT = 2.00,2.0,3.0, * height of protuberances by set

OPROT = 0.00,0.0,0.0, * offset of protuberances by set

$END

Figure 27. Sample Protuberance Input

Figure 28. Sample Missile with Protuberances

Protuberance axial forces are calculated in Missile Datcom only for zero angle of attack, and consequently, will

cause the corresponding pitching and yawing moments to remain constant with angle of attack. In order to avoid an

excessively long output, the for006.dat output file contains a breakdown of protuberance axial forces and moments

listed at zero angle of attack only. Figure 29 shows a section of the for006.dat output file with predictions

corresponding to the input from Fig. 27.

19


IV. Conclusions

The US Air Force Research Laboratory and the US Army Aviation and Missile Research, Development, and

Engineering Center released the 8/08 version of Missile Datcom. Significant changes to axial force calculations for

bodies with blunted, truncated, and low fineness ratio noses are included in this release. These changes correct

discontinuities in predicted forebody axial force at subsonic, transonic, and supersonic Mach numbers. In the

subsonic region, curve fits based on CFD results were used to capture trends for short conical noses and partially

truncated noses. The supersonic area rule was removed from the transonic portion of the code and replaced by a

combination of hybrid theory and SOSE theory. In the supersonic region, hybrid theory and SOSE theory were

blended based on results from a previous study.

The changes to axial force calculations introduced in the 8/08 version of Missile Datcom primarily impact

geometries with blunted, truncated, or low fineness ratio noses. Great care was taken to improve predictions for

certain geometries and Mach ranges while avoiding changes that would adversely affect regions with sufficient

prediction accuracy. Experimental test data show that Datcom 8/08 is more suitable than previous versions for axial

PROTUBERANCE AXIAL FORCE COEFFICIENT IS CALCULATED AT ZERO ANGLE OF

ATTACK AND ASSUMED CONSTANT FOR ALL ANGLES OF ATTACK. PROTUBERANCES

ARE CONSIDERED PART OF THE BODY WHEN CALCULATING TOTAL AXIAL FORCE.

PROTUBERANCE AXIAL FORCE IS INCLUDED IN THE TOTAL CONFIGURATION RESULTS.

---------- PROTUBERANCE CALCULATIONS (AT ZERO ANGLE OF ATTACK) ----------

LONG. NUMBER INDIVIDUAL TOTAL

NUMBER TYPE LOCATION (IN) CA CA

1 FAIRING 50.000 2 0.0052 0.0103

**** INDUCED MOMENT BREAKDOWN ****

PROTUBERANCE PHI = 0.000 CM = 0.0031 CLN = 0.0000

PROTUBERANCE PHI = 180.000 CM = -0.0031 CLN = 0.0000

2 VERTICAL CYLINDER 60.000 1 0.1323 0.1323


PROTUBERANCE PHI = 270.000 CM = 0.0000 CLN = -0.0794

3 FAIRING 70.000 3 0.0084 0.0251


PROTUBERANCE PHI = 60.000 CM = 0.0027 CLN = 0.0047

PROTUBERANCE PHI = 180.000 CM = -0.0054 CLN = 0.0000

PROTUBERANCE PHI = 300.000 CM = 0.0027 CLN = -0.0047

TOTAL CA DUE TO PROTUBERANCES = 0.1677

TOTAL CM DUE TO PROTUBERANCES = 0.0000

TOTAL CLN DUE TO PROTUBERANCES = -0.0794

Figure 29. Sample Protuberance Output

20


force prediction on bodies with short or partially truncated noses. Consistency of results with geometric trends was

greatly improved for the 8/08 version of Missile Datcom.

In addition, the ability to specify protuberance angular orientation was added to Missile Datcom 8/08. The

presence of protuberance angular orientation allows for the calculation of pitching and yawing moments associated

with the axial force acting on the protuberances.

21


Appendix A: Hybrid/SOSE Smoothing Routine Implemented in Missile Datcom 8/08

SUBROUTINE HYSOSE(MACH,HYSOFR)

C

C THIS SUBROUTINE CALCULATES THE FRACTION USED

C TO LINEARLY INTERPOLATE BETWEEN THE HYBRID

C PRESSURE DRAG AND THE SOSE PRESSURE DRAG.

C TRANSITION POINTS ARE BASED OF AIAA 83-0181.

C

C WRITTEN BY J. DOYLE, DYNETICS, INC.

C 8/1/07

C

C INPUTS

C

C MACH - MACH NUMBER AT WHICH PRESSURE DRAG IS TO

C BE DETERMINED

C

C OUTPUTS

C

C HYSOFR - SOSE PRESSURE DRAG FRACTION TO BE USED.

C 0.0 = 100% HYBRID THEORY

C 1.0 = 100% SOSE

C

INCLUDE 'comconst.inc'

INCLUDE 'comgeobo.inc'

INCLUDE 'comabodi.inc'

INCLUDE 'combody.inc'

C

INTEGER ILOOP

REAL MACH,HYSOFR,UPLIM,LOWLIM

REAL MAXANG,MAXSLP,MACSLP

C

C FIND UPPER LIMIT OF INTERPOLATION BY

C RECOMMENDATION IN AIAA 83-0181

C

UPLIM = SQRT(MACH**2.0-1)/0.4

C

C DETERMINE MAXIMUM SURFACE ANGLE ON NOSE

MAXSLP = 0.0

DO 1000 ILOOP = 1,TOTPTS

MAXSLP = MAX(MAXSLP,DRDX(ILOOP))

IF (XX(ILOOP) .GE. LNOSE) GO TO 1100

1000 CONTINUE

C

1100 MAXANG = ATAN(MAXSLP)

C

C IF TERMINAL ANGLE IS GREATER THAN MACH CONE ANGLE,

C USE 100% SOSE TO DETERMINE PRESSURE DRAG

IF (MAXANG .GE. ASIN(1/MACH)) THEN

HYSOFR = 1.0

C IF NOSE FINENESS RATIO IS GREATER THAN THAT OF THE

C UPPER LIMIT FOR SOSE, USE 100% HYBRID THEORY

ELSE IF (FRNOSE .GE. UPLIM) THEN

HYSOFR = 0.0

ELSE

22


C FIND A CORRESPONDING FINENESS RATIO FOR THE LOWER

C LIMIT OF THE INTERPOLATION. THIS IS THE THEORETICAL

C FINENESS RATIO OF A SIMILAR COMPRESSED NOSE WITH ITS

C TERMINAL ANGLE EQUAL TO THE MACH ANGLE

C

MACSLP = TAN(ASIN(1/MACH))

LOWLIM = MAXSLP/MACSLP*FRNOSE

C

C SET FRACTION OF SOSE PRESSURE DRAG TO BE USED

HYSOFR = (UPLIM-FRNOSE)/ (UPLIM-LOWLIM)

END IF

C

END

23


Acknowledgments

The author would like to thank William Blake of Air Force Research Laboratories for his invaluable guidance

and support in this effort.

References

1Hoerner, S. F., “Fluid Dynamic Drag,” Published by Author, 1965. 2Chafin, Jim, “User’s Guide for Bluff Body (BLUFBD) Aerodynamic Data Base,” TR1015, Prepared for the U.S. Army

Missile Command Aeroballistics Directorate by New Technology, Inc., July, 1979. 3Berglund, Hans, “Measurements of the Symmetric Aerodynamic Coefficients for Flat Faced Cylinders in the Angle of

Attack Regime 0 to 90 Degrees for Transonic and Supersonic Speeds,” FFA-TN-1984-04 4Drew, B., Jenn, A., “Pressure Drag Calculations on Axisymmetric Bodies of Arbitrary Moldline,” AIAA-90-0280, January,

1990. 5Neely, A., Auman, L., Blake, W., “Missile DATCOM Transonic Drag Improvements for Hemispherical Nose Shapes,”

AIAA 2003-3668, June, 2003. 6Vukelich, S.R., Jenkins, J.E., “Missile Datcom Status Report: Body and Fin Alone Methodology,” AIAA-83-0181, January,

1983. 7Vukelich, S. R., “Missile Datcom Volume 2: Body Alone Aerodynamic Methodology,” unpublished, March 1984. 8Riddle, D. B., Rosema, C. C., Auman, L. M., Technical Report AMR-SS-08-24, U.S. Army AMRDEC, Redstone Arsenal,

Alabama, June 2008. 9Blake, W. B., Missile Datcom: User’s Manual – 1997 FORTRAN 90 Version,” Air Force Research Laboratories Document

AFRL-VA-WP-TR-1998-3009, Feb. 1998. 10DeJarnette, F. R., Ford, C. P., Young, D. E., “Calculation of Pressures on Bodies at Low Angles or Attack,” AIAA Journal

of Spacecraft, Article 79-1552R, 1979. 11Devan, Leroy, “Inviscid, Nonaxisymmetric Body, Supersonic Aerodynamic Prediction,” AIAA-87-2296, 1987. 12Hayes, W. C., Henderson, W. P., “Some Effects of Nose Bluntness and Fineness Ratio on the Static Longitudinal

Aerodynamic Characteristics of Bodies of Revolution at Subsonic Speeds,” NASA TN D-650, Langley Research Center, Langley

Field, VA, February, 1961. 13Rosema C., Underwood, M., Auman, L., “Recent Fin Related Improvements for Missile DATCOM,” AIAA 2007-3937,

Dynetics Inc., Huntsville, AL, June, 2007. 14 Underwood, M., Rosema C., Wilks, B., Keenan, J., Auman, L., “Recent Improvements to Missile DATCOM,” AIAA

2007-3936, DESE Research Inc., Huntsville, AL, June, 2007.

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