By:

###### Izydor Kawa

Galaxy Scientific Corporation

2500 English Creek Ave., Bldg. C

Egg Harbor Twp., NJ 08234-5562, U.S.A.

Phone: (609) 645-0900; FAX: (609) 645-2881

izydor.kawa@galaxyscientific.com

Gordon F. Hayhoe

FAA William J. Hughes Technical Center

Airport Technology Research and Development Branch, AAR-410

Atlantic City International Airport, NJ 08405, U.S.A.

Phone: (609) 485- 8555; FAX: (609) 485-4845

gordon.hayhoe@tc.faa.gov

PRESENTED AT THE 2002 FEDERAL AVIATION ADMINISTRATION AIRPORT TECHNOLOGY
TRANSFER CONFERENCE

05/02

## ABSTRACT

A computer program was developed for computing flexible and rigid
pavement Aircraft Classification Numbers (ACNs) according to Annex 14 of
the ICAO Airport Pavement Design Manual. The computer subroutines listed
in Appendix 4 of the ICAO manual have been implemented in the computer
program, and it was shown that these implementations accurately
reproduce the ACNs computed by the ICAO programs. The program contains
an internal library of aircraft covering most of the large commercial
and military aircraft currently in operation and those included in the
ICAO manual. A new aircraft configuration can be added to an external
library. The user of the program can also modify airplane gear
configurations by adding and removing wheels or moving wheels to any
arbitrary location. The computer program also has the capability of
calculating flexible and rigid pavement thicknesses. In the case of
rigid pavements, calculation of slab thickness implements the Portland
Cement Association (PCA) method based on slab interior stress or
implements the Federal Aviation Administration (FAA) Westergaard edge
stress procedure as is implemented in the design charts in Advisory
Circular (AC) 150/5320-6D. Two triple twin tandems closely spaced were
analyzed. It has been found that the influence of the second twin tandem
on slab thickness is negligible based on the H51 model implemented in
the computer program.

**INTRODUCTION**

Airport operators need a comprehensive tool for evaluation of pavement
thickness and strength. COMFAA is a general-purpose computer program
that operates in two computational modes: Aircraft Classification Number
(ACN) Computation Mode and Pavement Design Mode. In ACN Computation
Mode, COMFAA:

-   Calculates the ACN number for aircraft on flexible pavements.

-   Calculates the ACN number for aircraft on rigid pavements.

-   Calculates flexible pavement thickness based on the California
    Bearing Ratio (CBR) method in Advisory Circular (AC) 150/5320-6D for
    default values of CBR of 15, 10, 6, and 3.

-   Calculates rigid pavement slab thickness based on the Portland
    Cement Association (PCA) method for default values of *k* of 552.6,
    294.7, 147.4, and 73.7 lb/in^3^.

In Pavement Design Mode, COMFAA:

-   Calculates flexible pavement thickness based on the CBR method in AC
    150/5320-6D for a CBR value specified by the user.

-   Calculates rigid pavement slab thickness based on AC 150/5320-6D
    \[2\] for a *k* value specified by the user.

The above calculations can be done for any type of aircraft gear
configuration. The user of the program can also modify airplane gear
configurations by adding and removing wheels or moving wheels to any
arbitrary location. The input data can be entered and results can be
viewed in English and Metric units. This paper describes how the program
was developed.

## ACN NUMBER FOR FLEXIBLE AND RIGID PAVEMENTS

COMFAA contains two procedures for calculating the ACN number for rigid
and flexible pavements, which are based on two Fortran computer programs
adopted from the ICAO Aerodrome Design Manual \[1\]. Users may calculate
the ACN number for any aircraft in the COMFAA library, which consists of
internal and external libraries. The user has the capability to add
aircraft only to the external library. The internal library consists of
the following groups: generic, Airbus, Boeing, McDonnell Douglas, other
commercial, and military aircraft groups. Overall, there are 90 types of
aircraft available in the internal library.

## Installation of THE RIGID PAVEMENT Design Model from AC 150/5320‑6D

The following modifications were made to enable COMFAA to calculate
rigid pavement thickness under a number of coverages of a design
aircraft according to AC 150/5320-6D \[2\].

# **Installation of Visual Basic Version of H51**

H51 \[3\] is a Fortran computer program which calculates slab edge
stresses resulting from loads applied by aircraft landing gear. It is
based on the theory of a semi-infinite plate on an elastic foundation.
The H51 Fortran program was converted to Visual Basic, and the new
program (TestH51) was thoroughly debugged to ensure that the results
were the same as those from H51 within numerical roundoff. TestH51 was
then installed into COMFAA and modified so that the aircraft
characteristics may be read in from the aircraft library. All of the
necessary input to TestH51 is provided by the COMFAA user through the
COMFAA graphical interface.

# **Extension of H51 Capabilities**

H51 has a capability to directly calculate slab edge stresses for the
following gear configurations: single wheel, twin, dual twin (dual),
single tandem, twin tandem, dual twin tandem, and triple twin tandem
(tridem). However, the capability has been expanded to calculate the
slab edge stress for any gear configuration using the principle of
superposition.

The calculation of the slab edge stress *σ~A~*~1~, for a wheel located
at coordinates *x* and *y*, is accomplished in the following steps as
shown in figure 1:

-   Calculate the slab edge stress *σ~A~*~2~ for a twin tandem with
    x-transverse spacing between the tires, and y-longitudinal spacing
    between the tires.

-   Calculate the slab edge stress *σ~A~*~3~ for a single tandem with
    y-longitudinal spacing between the tires.

-   Calculate the slab edge stress *σ~A~*~4~ for a single wheel
    displaced a distance x from the point of calculated stress.

-   Calculate the slab edge stress *σ~A~*~1~ for a wheel located at
    coordinates *x* and *y* according to the formula *σ~A~*~1~ =
    *σ~A~*~2~ - *σ~A~*~3~ - *σ~A~*~4.~

For gear configurations not included in H51, COMFAA performs stress
calculations for all of the individual wheels of the gear. The final
slab edge stress from the gear is calculated by the summation of all of
the stresses produced by the individual wheels.

Figure 1. Calculation of slab edge stress for any wheel location using
the principle of superposition.

Initially, the location of maximum stress is not known and can be
located either under one of the wheels or at some location between the
wheels. A subroutine was written based on a golden section search
procedure \[4\], which searches for the maximum stress along the slab
edge. Two cases were analyzed, as shown in figure 2. First, when a gear
is located perpendicular to the slab edge, the search is conducted along
the *x*-axis between points "A" and "B." Second, when a gear is located
parallel to the slab edge, the search is conducted along the *y*-axis
between points "C" and "D".

Figure 2. Search area for maximum stress location.

## Calculation of Slab Thickness

The calculated maximum slab edge stress for a specified slab thickness
is compared with the maximum allowable stress specified for the PCC. If
the calculated maximum stress is significantly different from the
maximum allowable stress, the slab thickness is adjusted. For example,
the Federal Aviation Administration (FAA) computer program for rigid
airport pavement design R805FAA uses an approximation method to estimate
PCC slab edge stresses and obtains PCC slab thickness by an iterative
method. A review of the source code for R805FAA shows that the obtained
thickness is then adjusted by a coefficient which is calculated based on
the number of aircraft coverages. This represents the PCC fatigue
failure model. A similar approach was used in a subroutine of COMFAA,
the difference being that the subroutine uses the H51 code for
calculating slab edge stresses. The purpose of this subroutine is to
find the slab thickness, *H~Slab~*, for which the slab edge stress,
calculated by COMFAA, satisfies the following equation:

$\sigma(H_{\text{Slab}}) \leq \frac{R_{C}}{1\text{.}3 \times 0\text{.}\text{75}}$
(1)

where:

  ---------------- ---------------------------------------------------------------
  *σ*(*H~Slab~*)   = maximum tensile edge stress at the bottom of the slab for
                   slab thickness *H~Slab~*

  *R~C~*           = flexural strength of the PCC

  1.3              = safety factor

  0.75             = reduction factor based on assumption that a joint transfers
                   25% of the load to the other side of the joint
  ---------------- ---------------------------------------------------------------

The slab edge stresses are calculated for gear loads located either
parallel or perpendicular to the joint. From the two calculated stresses
the maximum stress is selected which satisfies Equation 1. A procedure,
RTBIS \[4\], implementing a bisection method, was translated to Visual
Basic to find the slab thickness *H~Slab~* for which the maximum slab
edge stress *σ* is calculated by COMFAA with the precision of 0.01 in.
Figure 3 presents a flow chart for the algorithm implemented in COMFAA.

Initially, the algorithm determines a slab thickness interval within
which the solution exists. It then starts a loop. The maximum slab edge
stress is evaluated in the middle of the interval. If the maximum stress
is higher than the maximum allowable stress, a new interval is taken
between the midpoint and the upper bound of the interval and the stress
is evaluated at the midpoint of the new interval HSlab = HSlab + DH,
where DH is half the distance between HSlab and the upper bound of the
interval. If the maximum stress is lower than the maximum allowable
stress, then the new interval is taken between the lower bound of the
interval and the midpoint, and the stress is evaluated at the midpoint
of the new interval HSlab = HSlab -- DH, where DH is half the distance
between HSlab and the lower bound of the interval. The loop continues
until the size of the interval is smaller than 0.01 inch. Finally, the
slab thickness, *H~Slab~*, is adjusted by a factor *α* as applied in the
following equation:

$H_{\text{Adj}\text{.}\ \text{Slab}} = \alpha \times H_{\text{Slab}}$
(2)

where *α* is a function for adjusting slab thickness by using the
fatigue curve developed by the U.S. Army Corps of Engineers from test
track data and observations of in-service pavements calculated according
to the following equations \[5\]:

$\alpha = 1 + 0\text{.}\text{15603}\text{*log}_{\text{10}}\left( \frac{\text{COVERAGE}}{\text{5000}} \right)\begin{matrix}
 & \begin{matrix}
\text{for} & (\text{COVERAGE} \geq \text{5000})
\end{matrix}
\end{matrix}$ (3)

or

$\alpha = 1 + 0\text{.}\text{07058}\text{*log}_{\text{10}}\left( \frac{\text{COVERAGE}}{\text{5000}} \right)\begin{matrix}
 & \begin{matrix}
\text{for} & (\text{COVERAGE} < \text{5000})
\end{matrix}
\end{matrix}$ (4)

Figure 3. Algorithm for calculating slab thickness.

![](media/image2.png){width="4.5in" height="3.375in"}

Figure 4. COMFAA graphical interface with design thickness result.

Figure 4 presents a COMFAA screen with a design thickness result. COMFAA
runs calculations for rigid pavements in two different computational
modes:

1.  The ACN Computation Mode: ACN calculations and slab thickness
    calculations based on the slab interior stress as specified in
    reference 1.

2.  The Pavement Design Mode: slab thickness calculations that implement
    the FAA procedure based on Westergaard edge stress as is implemented
    in the design charts in AC 150/5320-6D \[2\].

The user selects the computational mode by selecting the option button
in the computational mode frame as shown in figure 4. When the user
selects the option button labeled "ACN Computation" and clicks the
button labeled "ACN [R]{.underline}igid," PCC slab thicknesses and ACNs
are calculated for four pavement structures having subgrades with the
specified *k* values (552.6, 294.7, 147.4, and 73.7 lb/in^3^). The
calculations are based on the slab interior stress.

If the user selects the option button labeled "Pavement Design" and
clicks the button labeled "Rigid Design," the program computes PCC slab
thickness for the *k* value specified by the user and based on the slab
edge stress. The user specifies the *k* value by clicking on the field
labeled "k lb/in\^3" and typing the *k* value in a message box.

For the case shown in figure 4, the design thickness of the slab is
17.90 inches on a subgrade with a *k* value of 100 lb/in^3^ and loaded
with a 400,000 lb dual tandem gear aircraft and 10,000 coverages, in
which coverages may be obtained from the total pass number divided by
the pass/coverage ratio in AC 150/5320-6D \[2\].

# **Reliability of COMFAA**

The reliability of COMFAA was checked with respect to the calculation of
ACNs, slab edge stress, and slab thickness.

**ACNs Calculated Using the ComFAA, ACNR, and ACNF Programs**

The results are presented in Tables 1 and 2 and show that for some
airplanes there are minor differences between ACNs calculated by COMFAA
and those obtained from the ICAO Design Manual. These differences could
be attributed to rounding of the ACNs in the ICAO Design Manual. A
comparison with programs ACNR and ACNF \[6 and 7\], which are two
computer programs developed based on the ICAO Design Manual \[1\], was
made to check for similar differences. For most of the gear
configurations that can be classified as single, dual, tandem, and dual
tandem, the differences between the ACNs calculated by COMFAA and those
listed in the ICAO Design Manual are very small. In most cases, ICAO
ACNs look like rounded numbers calculated by COMFAA. For example, for
flexible pavement (subgrade CBR=15), the COMFAA for the A310 aircraft is
35.9, the ICAO number is 36, and the ACNF number is 35.80. This
indicates that the ACN calculated by ACNF supports those calculated by
COMFAA. Therefore, the ACN calculated by COMFAA can be considered
reliable and the program can be used for the calculation of ACNs for the
gear configurations which can be classified as single, dual, tandem, and
dual tandem.

For the more complex gear configurations, COMFAA ACNs are either similar
to ICAO ACNs and/or to ACNF ACNs or ACNR ACNs, except for the Canadair
CL 44 aircraft for rigid pavements. For the Canadair CL 44 aircraft on
rigid pavements, the ICAO and the ACNR ACNs are similar. However, ACNs
calculated by COMFAA are higher. The difference needs further study.

Table 1. ACNs for selected aircraft on rigid pavements.

<table style="width:100%;">
<colgroup>
<col style="width: 16%" />
<col style="width: 6%" />
<col style="width: 6%" />
<col style="width: 6%" />
<col style="width: 6%" />
<col style="width: 9%" />
<col style="width: 5%" />
<col style="width: 5%" />
<col style="width: 6%" />
<col style="width: 7%" />
<col style="width: 7%" />
<col style="width: 7%" />
<col style="width: 7%" />
</colgroup>
<tbody>
<tr class="odd">
<td>Aircraft type</td>
<td colspan="4"><p>ACN by COMFAA</p>
<p>Subgrade <em>k</em> [MN/m<sup>3</sup>]</p></td>
<td colspan="4">ACN by ICAO Design Manual Subgrade <em>k</em>
[MN/m<sup>3</sup>]</td>
<td colspan="4"><p>ACN by ACNR [6]</p>
<p>Subgrade <em>k</em> [MN/m<sup>3</sup>]</p></td>
</tr>
<tr class="even">
<td></td>
<td>150</td>
<td>80</td>
<td>40</td>
<td>20</td>
<td>150</td>
<td>80</td>
<td>40</td>
<td>20</td>
<td>150</td>
<td>80</td>
<td>40</td>
<td>20</td>
</tr>
<tr class="odd">
<td>A310</td>
<td>32.4</td>
<td>38.7</td>
<td>46.2</td>
<td>53.2</td>
<td>33</td>
<td>39</td>
<td>46</td>
<td>54</td>
<td>33</td>
<td>38.4</td>
<td>45.4</td>
<td>52.3</td>
</tr>
<tr class="even">
<td>A320 DT</td>
<td>16.5</td>
<td>19.8</td>
<td>23.6</td>
<td>27.2</td>
<td>18</td>
<td>21</td>
<td>24</td>
<td>28</td>
<td>16.7</td>
<td>19.7</td>
<td>23.3</td>
<td>26.9</td>
</tr>
<tr class="odd">
<td>Caravelle 10</td>
<td>13.7</td>
<td>16.4</td>
<td>19.3</td>
<td>21.9</td>
<td>15</td>
<td>17</td>
<td>20</td>
<td>22</td>
<td>32.8</td>
<td>33.7</td>
<td>34.7</td>
<td>35.6</td>
</tr>
<tr class="even">
<td>Canadair CL 44</td>
<td>30.0</td>
<td>35.2</td>
<td>40.6</td>
<td>45.4</td>
<td>25</td>
<td>30</td>
<td>35</td>
<td>40</td>
<td>25.3</td>
<td>29.9</td>
<td>35.4</td>
<td>40.5</td>
</tr>
<tr class="odd">
<td>CV 880 M</td>
<td>25.8</td>
<td>30.8</td>
<td>35.8</td>
<td>40.3</td>
<td>26</td>
<td>31</td>
<td>36</td>
<td>41</td>
<td>25.7</td>
<td>30.0</td>
<td>34.9</td>
<td>39.3</td>
</tr>
<tr class="even">
<td>MD-87</td>
<td>43.7</td>
<td>46.0</td>
<td>48.0</td>
<td>49.7</td>
<td>45</td>
<td>47</td>
<td>49</td>
<td>50</td>
<td>43.7</td>
<td>46.0</td>
<td>48.1</td>
<td>49.7</td>
</tr>
<tr class="odd">
<td>DC-10-15</td>
<td>48.5</td>
<td>57.2</td>
<td>68.5</td>
<td>79.7</td>
<td>48</td>
<td>56</td>
<td>67</td>
<td>74</td>
<td>48.7</td>
<td>56.3</td>
<td>67.0</td>
<td>78.0</td>
</tr>
<tr class="even">
<td>IL76T</td>
<td>11.0</td>
<td>13.2</td>
<td>15.4</td>
<td>14.4</td>
<td>38</td>
<td>38</td>
<td>38</td>
<td>39</td>
<td>10.9</td>
<td>12.2</td>
<td>14.0</td>
<td>13.6</td>
</tr>
<tr class="odd">
<td>L1011-1</td>
<td>44.3</td>
<td>51.7</td>
<td>61.7</td>
<td>72.2</td>
<td>45</td>
<td>52</td>
<td>62</td>
<td>73</td>
<td>46.3</td>
<td>51.9</td>
<td>61.1</td>
<td>71.3</td>
</tr>
<tr class="even">
<td>TU154B</td>
<td>17.5</td>
<td>23.8</td>
<td>30.4</td>
<td>36.2</td>
<td>19</td>
<td>25</td>
<td>32</td>
<td>38</td>
<td>15.8</td>
<td>18.2</td>
<td>23.6</td>
<td>29.0</td>
</tr>
</tbody>
</table>

Table 2. ACNs for selected aircraft on flexible pavements.

<table>
<colgroup>
<col style="width: 16%" />
<col style="width: 6%" />
<col style="width: 6%" />
<col style="width: 6%" />
<col style="width: 8%" />
<col style="width: 6%" />
<col style="width: 5%" />
<col style="width: 5%" />
<col style="width: 9%" />
<col style="width: 7%" />
<col style="width: 7%" />
<col style="width: 7%" />
<col style="width: 7%" />
</colgroup>
<tbody>
<tr class="odd">
<td>Aircraft type</td>
<td colspan="4"><p>ACN by COMFAA</p>
<p>Subgrade CBR</p></td>
<td colspan="4">ACN by ICAO Design Manual Subgrade CBR</td>
<td colspan="4"><p>ACN by ACNF [7]</p>
<p>Subgrade CBR</p></td>
</tr>
<tr class="even">
<td></td>
<td>15</td>
<td>10</td>
<td>6</td>
<td>3</td>
<td>15</td>
<td>10</td>
<td>6</td>
<td>3</td>
<td>15</td>
<td>10</td>
<td>6</td>
<td>3</td>
</tr>
<tr class="odd">
<td>A310</td>
<td>35.9</td>
<td>39.7</td>
<td>48.1</td>
<td>63.2</td>
<td>36</td>
<td>40</td>
<td>48</td>
<td>64</td>
<td>35.80</td>
<td>39.73</td>
<td>48.11</td>
<td>63.18</td>
</tr>
<tr class="even">
<td>A320 DT</td>
<td>17.6</td>
<td>19.2</td>
<td>23.1</td>
<td>31.7</td>
<td>18</td>
<td>19</td>
<td>23</td>
<td>32</td>
<td>17.63</td>
<td>19.22</td>
<td>23.06</td>
<td>31.69</td>
</tr>
<tr class="odd">
<td>Caravelle 10</td>
<td>14.7</td>
<td>16.5</td>
<td>19.3</td>
<td>23.1</td>
<td>15</td>
<td>17</td>
<td>19</td>
<td>23</td>
<td>13.88</td>
<td>15.49</td>
<td>18.72</td>
<td>22.89</td>
</tr>
<tr class="even">
<td>Canadair CL 44</td>
<td>31.5</td>
<td>35.6</td>
<td>40.3</td>
<td>48.1</td>
<td>27</td>
<td>30</td>
<td>36</td>
<td>47</td>
<td>31.52</td>
<td>35.61</td>
<td>40.27</td>
<td>48.13</td>
</tr>
<tr class="odd">
<td>CV 880 M</td>
<td>26.5</td>
<td>30.6</td>
<td>35.7</td>
<td>44.0</td>
<td>27</td>
<td>31</td>
<td>36</td>
<td>44</td>
<td>26.53</td>
<td>30.62</td>
<td>35.77</td>
<td>43.98</td>
</tr>
<tr class="even">
<td>MD-87</td>
<td>38.6</td>
<td>41.1</td>
<td>46.0</td>
<td>49.2</td>
<td>39</td>
<td>42</td>
<td>46</td>
<td>50</td>
<td>37.89</td>
<td>39.13</td>
<td>42.59</td>
<td>46.42</td>
</tr>
<tr class="odd">
<td>DC-10-15</td>
<td>55.8</td>
<td>61.5</td>
<td>73.4</td>
<td>100.2</td>
<td>55</td>
<td>61</td>
<td>72</td>
<td>100</td>
<td>55.39</td>
<td>60.85</td>
<td>72.15</td>
<td>98.88</td>
</tr>
<tr class="even">
<td>IL76T</td>
<td>9.0</td>
<td>10.4</td>
<td>12.5</td>
<td>16.5</td>
<td>37</td>
<td>40</td>
<td>45</td>
<td>53</td>
<td>8.23</td>
<td>9.31</td>
<td>10.90</td>
<td>13.96</td>
</tr>
<tr class="odd">
<td>L1011-1</td>
<td>51.9</td>
<td>56.4</td>
<td>66.1</td>
<td>90.2</td>
<td>52</td>
<td>56</td>
<td>66</td>
<td>91</td>
<td>51.95</td>
<td>56.42</td>
<td>66.13</td>
<td>90.19</td>
</tr>
<tr class="even">
<td>TU154B</td>
<td>19.2</td>
<td>22.4</td>
<td>28.4</td>
<td>37.1</td>
<td>20</td>
<td>24</td>
<td>30</td>
<td>38</td>
<td>19.16</td>
<td>22.35</td>
<td>28.35</td>
<td>37.02</td>
</tr>
</tbody>
</table>

# **Slab Thickness Calculated Using COMFAA and AC 150/5320-6D**

Seven cases were analyzed to compare the design thicknesses obtained
from COMFAA, AC 150/5320-6D, and R805FAA. The input data for these cases
is included in Table 3. Table 4 presents a comparison of design
thicknesses obtained from the three sources. The last column in Table 4
shows the difference between the design thickness obtained from R805FAA
and from COMFAA. The maximum difference between R805FAA and COMFAA
results is 0.34 in. in thickness design. It can be concluded that COMFAA
produces acceptable results.

Table 3. Input data for thickness designs.

+---+------------+--------+------+--------+----+------+-----+------+
| L | Air        | Annual | P    | C      | *  | Conc | G   | Tire |
| p | craft/Gear |        | ass/ | overag | k* | rete | ear | Con  |
|   | Con        | Depa   | Cov. | es^\*^ |    |      | Wei | tact |
|   | figuration | rtures | R    |        |    | Flex | ght | Area |
|   |            |        | atio |        |    | ural |     |      |
|   |            |        |      |        |    |      |     |      |
|   |            |        |      |        |    | Stre |     |      |
|   |            |        |      |        |    | ngth |     |      |
+---+------------+--------+------+--------+----+------+-----+------+
|   |            |        |      |        | lb | psi  | lbs | i    |
|   |            |        |      |        | /i |      |     | n^2^ |
|   |            |        |      |        | n^ |      |     |      |
|   |            |        |      |        | 3^ |      |     |      |
+---+------------+--------+------+--------+----+------+-----+------+
| 1 | Single     | 1200   | 5.18 | 4,633  | 1  | 750  | 35, | 29   |
|   | Wheel      |        |      |        | 00 |      | 625 | 6.87 |
+---+------------+--------+------+--------+----+------+-----+------+
| 2 | Dual Wheel | 1200   | 3.48 | 6,897  | 1  | 750  | 95, | 23   |
|   |            |        |      |        | 00 |      | 000 | 7.50 |
+---+------------+--------+------+--------+----+------+-----+------+
| 3 | Dual       | 6000   | 3.68 | 32,609 | 2  | 700  | 1   | 23   |
|   | Tandem     |        |      |        | 00 |      | 90, | 7.50 |
|   |            |        |      |        |    |      | 000 |      |
+---+------------+--------+------+--------+----+------+-----+------+
| 4 | A-300      | 6000   | 3.51 | 34,188 | 2  | 700  | 1   | 20   |
|   | Model B2   |        |      |        | 00 |      | 42, | 7.47 |
|   |            |        |      |        |    |      | 500 |      |
+---+------------+--------+------+--------+----+------+-----+------+
| 5 | B-747 SP   | 15000  | 3.70 | 81,081 | 50 | 800  | 1   | 21   |
|   |            |        |      |        |    |      | 66, | 0.00 |
|   |            |        |      |        |    |      | 250 |      |
+---+------------+--------+------+--------+----+------+-----+------+
| 6 | B-767      | 25000  | 3.90 | 1      | 3  | 650  | 1   | 20   |
|   |            |        |      | 28,205 | 00 |      | 42, | 2.46 |
|   |            |        |      |        |    |      | 500 |      |
+---+------------+--------+------+--------+----+------+-----+------+
| 7 | DC-10-10   | 25000  | 3.64 | 1      | 3  | 650  | 2   | 29   |
|   |            |        |      | 37,363 | 00 |      | 13, | 4.00 |
|   |            |        |      |        |    |      | 750 |      |
+---+------------+--------+------+--------+----+------+-----+------+

^\*^ Coverages are determined by multiplying annual departures by 20 and
dividing that product by the pass-to-coverage ratio \[2\].

Table 4. Results of thickness designs.

+----+---------------+-----+----------+-----------+-------------------+
| Lp | Aircraft/Gear | Des |          |           | Difference        |
|    | Configuration | ign |          |           |                   |
|    |               | Th  |          |           | H~R805FAA~ -      |
|    |               | ick |          |           | H~COMFAA~         |
|    |               | nes |          |           |                   |
|    |               | s - |          |           |                   |
|    |               | H   |          |           |                   |
+----+---------------+-----+----------+-----------+-------------------+
|    |               | 6D  | R805FAA  | COMFAA    |                   |
+----+---------------+-----+----------+-----------+-------------------+
|    |               | in. | in.      | in.       | in.               |
+----+---------------+-----+----------+-----------+-------------------+
| 1  | Single Wheel  | 1   | 10.00    | 9.98      | 0.02              |
|    |               | 0.2 |          |           |                   |
+----+---------------+-----+----------+-----------+-------------------+
| 2  | Dual Wheel    | 1   | 15.42    | 15.30     | 0.12              |
|    |               | 5.3 |          |           |                   |
+----+---------------+-----+----------+-----------+-------------------+
| 3  | Dual Tandem   | 1   | 16.99    | 16.65     | 0.34              |
|    |               | 7.0 |          |           |                   |
+----+---------------+-----+----------+-----------+-------------------+
| 4  | A-300 Model   | 1   | 12.96    | 12.72     | 0.24              |
|    | B2            | 3.0 |          |           |                   |
+----+---------------+-----+----------+-----------+-------------------+
| 5  | B-747 SP      | 1   | 17.55    | 17.43     | 0.12              |
|    |               | 7.8 |          |           |                   |
+----+---------------+-----+----------+-----------+-------------------+
| 6  | B-767         | 1   | 12.62    | 12.54     | 0.08              |
|    |               | 2.4 |          |           |                   |
+----+---------------+-----+----------+-----------+-------------------+
| 7  | DC-10-10      | 1   | 15.27    | 15.12     | 0.15              |
|    |               | 5.5 |          |           |                   |
+----+---------------+-----+----------+-----------+-------------------+

# **Analysis of Two Closely Spaced Triple Twin Tandems Using COMFAA**

Figure 5 presents dimensions of two closely spaced triple twin tandems
which are analyzed with COMFAA. The purpose of the analysis is to
determine the effect of a second triple twin tandem on the maximum slab
edge stress. The single-tire load for the analyzed case is 58,852.405
lbs, and the tire pressure is 194 psi.

Figure 5. Two closely spaced triple twin tandems.

Figures 6 and 7 show the results for two different cases:

-   Case 1: slab thickness of 14.90 inches, 5,000 coverages and subgrade
    modulus *k* = 100 pci.

-   Case 2: slab thickness of 12.62 inches, 5,000 coverages, and
    subgrade modulus *k* = 200 pci.

Figures 6 and 7 show the contribution of each individual wheel to the
maximum slab edge stress at the bottom of the slab. In both cases the
contribution of one triple twin tandem to the maximum slab edge stress
is significant while the contribution of a second triple twin tandem is
negligible. It can be concluded that it is sufficient to consider only
one triple twin tandem when determining the maximum slab edge stress
using the H51 model.

Figure 6. Contribution of individual wheels to slab edge stress at
location "A" for two triple twin tandems (slab thickness = 14.90 inches,
coverages = 5,000, and *k* = 100 pci).

Figure 7. Contribution of individual wheels to slab edge stress at
location "A" for two triple twin tandems (slab thickness = 12.62 inches,
coverages = 5,000, and *k* = 200 pci).

The contribution of a single wheel to the edge stress, based on the
location of the wheel, is shown in figure 8. The figures show that the
contribution of the wheel to the edge stress is insignificant when the
wheel is located more than 190 inches from the point of edge stress
evaluation.

![](media/image3.wmf)

Figure 8. 3-d surface of edge stress depending on wheel position at
coordinates *x* and *y* (slab thickness = 12.62 inches, coverages =
5,000, and *k* = 200 pci).

**SUMMARY**

The FAA has developed a program with multiple purposes including
calculation of ACN numbers for aircraft on flexible and rigid pavements
and calculation of flexible and rigid pavement thicknesses based on
different models. It is a user-friendly tool for airport operators and
pavement engineers.

**Acknowledgements/Disclaimer**

The work described in this paper was supported by the FAA Airport
Technology Research and Development Branch, Dr. Satish K. Agrawal,
Manager. The contents of the paper reflect the views of the authors, who
are responsible for the facts and accuracy of the data presented within.
The contents do not necessarily reflect the official views and policies
of the FAA. This paper does not constitute a standard, specification, or
regulation.

## References

1.  "Aerodrome Design Manual: Part 3 Pavements," Second Edition, Doc
    9157-AN/901 Part 3, International Civil Aviation Organization, 1983.

2.  "Airport Pavement Design and Evaluation," AC 150/5320-6D, July 7,
    1995.

3.  Kreger, W.C., "Computerized Aircraft Ground Flotation
    Analysis-Edge-Loaded Rigid Pavement," General Dynamics Research
    Program, Task RDP 414-61-506, January 1967.

4.  Press, W.H., Flannery B.P., Teukolsky, S.A., and Vettering, W.T.,
    "Numerical Recipes: The Art of Scientific Computing," Cambridge
    University Press, 1986.

5.  R805FAA Computer Program "Computer Aided Design for Rigid Airport
    Pavements (R805FAA)" Department of Transportation, Federal Aviation
    Administration, Washington, D.C., May 31, 1988.

6.  ACNR computer program "ICAO Aircraft Classification Number (ACN)
    Analysis for Aerodrome Pavements," International Civil Aviation
    Organization (ICAO), Aerodromes, Air Routes and Ground Aids Section.

7.  ACNF computer program "ICAO Aircraft Classification Number (ACN)
    Analysis for Aerodrome Pavements," International Civil Aviation
    Organization (ICAO), Aerodromes, Air Routes and Ground Aids Section.