fudge 2.0_allen_sie909_final_revised 25 april

FUDGE 2.0

Fuel Delivery Gross Weight Estimator Version 2.0

Fuel Estimation Modeling Study For C-17A Globemaster Personnel Mass Exit Airdrop Missions

Keith Allen U.S. Army Test and Evaluation Command

U.S. Army Yuma Proving Ground Yuma Test Center, Arizona

Produced for the U.S. Army and Air Force Air Drop Community SIE 909 Master’s Committee

University of Arizona Department of Systems and Industrial Engineering

Masters Project

April 2015

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TABLE OF CONTENTS

SECTION 1. INTRODUCTION 1.1 System Description……... ………………………………………………….……...........……1 1.2 Stakeholders……...…………………………………………………………………............…1 1.3 Test Program History and Benefits to User………………………………………...................2 1.4 Problem Statement, Objectives and Modeling Methodology………………………................3 1.5 Conclusions……........................................................................................................................5 1.6 Recommendations and Future Improvements………………...............................................…5 SECTION 2. FUEL CONSUMPTION MODEL VERSION 2 2.1 Factors Affecting Fuel Consumption………………….............................................................7 2.2 Model Development and Definition of Terms………………..…...........................................10 2.3 Model Biases and Assumptions…...........................................................................................18 2.4 Example Usage of Model.........................................................................…............................20 2.5 Model Verification…...............................................................................................................22 2.6 Fuel Consumption Modeling Tool…………..…………………………...…...…...................28 SECTION 3. APPENDICES

A. References…...…............................................................................................................A-1 B. Additional Data……...…................................................................................................B-1 C. Model Definition and Units………...…..........................................................................C-1

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ABSTRACT

The objective of the Fuel Delivery Gross Weight Estimator (FUDGE) 2.0 is to update and improve a fuel consumption and cost estimation model to more accurately forecast fuel requirements when planning personnel mass exit airdrop missions for the C-17 aircraft. The study is an update of FUDGE version 1.0, which was originally produced in July 2014 with limited numbers of empirical data points. Version 2.0 assesses using cost driving factors such as airspeed, gross aircraft weight and distance flown to build an accurate forecast for fuel consumption and cost, based on a new set of empirical flight data, while simplifying the equation from the original version. One of the major material cost drivers for the U.S. Air Force and Army airborne community planning tactical operations around the world, is availability of fuel resources. Testers, project managers and tactical mission commanders alike must be able to accurately forecast how much fuel will be required to execute a personnel mass exit airdrop. This in turn drives other tactical variables such as projection of force into enemy territory, where to set up refueling bases and how much material must be on hand to support the tactical airborne and ground missions.

SECTION 1. INTRODUCTION

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1.1 SYSTEM DESCRIPTION

The C–17 Globemaster III aircraft is the United States Air Force’s (USAF) main long range, heavy transport aircraft. It has a high wing lift and can deploy up to 102 paratroopers in a single pass from the troop doors. It can also carry over 170,000 pounds (lb.) of palletized cargo and vehicles. It has a maximum speed of 450 knots and a maximum range of over 2,400 nautical miles and is powered by four Pratt and Whitney F117–PW–100 turbo fans. The C–17 is capable of landing and taking off on improved and unimproved runway surfaces. Figure 1.1–1 shows the C–17 aircraft.

Figure 1.1–1. C–17 Globemaster III 1.2 STAKEHOLDERS U.S. Army Test and Evaluation Command (ATEC) authorized this Developmental Test (DT) effort under the ATEC project No. 2013–DT–YPG–SOSPT–F3184. Funding was managed by Program Manager-Soldier Clothing and Individual Equipment (PM–SCIE) at Natick Soldier Research, Development and Engineering Center. However, this test program was not a PM–SCIE program since it did not test a material solution. The program was managed by ATEC (Yuma Test Center) and reported directly to Department of the Army G–3/5/7 staff. Additionally, due to the nature of the funding source and visibility, the program was on the oversight list for the Office of the Secretary of Defense (OSD) Director of Operational Test and Evaluation (DOT&E). The requirements for this program have been developed by the YTC test team and coordinated directly with DA, DOT&E and the U.S. Army user community through the Test Program Working Group (TPWG).


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The end item user for this project consists of the 18th Airborne Corps and the 75th Ranger Regiment. The test objectives and requirements for this project were derived directly from a user defined operational requirements statement stated in Appendix A, Reference 2 (app A, ref 2). 1.3 TEST PROGRAM HISTORY AND BENEFITS TO USER

a. Program History For a complete history of the C-17 IGW/FSR program, see Ref. 1 in Appendix A.

In January 2012, the U.S. Army 75th Ranger Regiment staffed a memorandum requesting

to increase the C–17 total gross weight and to reduce the formation spacing (app A, ref 2). As a result of this request, YTC developed a Scope of Work (SOW) Rough Order of Magnitude (ROM) cost estimate to assess the risk of increasing the C–17 gross weight and reduced formation spacing study. Based on the ATEC SOW and ROM cost estimate, the Department of the Army requested funding. In May 2012, the U.S. Army Vice Chief of Staff requested USAF support of the test program, which the USAF subsequently concurred with. The USAF AMC Test and Evaluation was then tasked to support. A Failure Definition Scoring Criteria (FDSC) (app A, ref 4) were generated by YTC to define the roles, responsibilities, and failure definitions between USAF AMC TES and ATEC. The results of the test project are documented in app A, ref 1 and 14.

The author of the study presented in this document conducted an initial development of

fuel usage during IGW and FSR testing as a parallel effort in FUDGE version 1.0 in 2014 to fulfill a requirement for the SIE 564 Cost Estimation course at the University of Arizona. Version 1.0 utilized empirical flight data from the C-17 IGW study conducted in 2013. In April 2014, the YTC test team, led by the author of this study, performed 143 personnel airdrop flights with a C-17 in both daytime and nighttime conditions. The objective of this effort was to collect wing tip vortex data for the on-going C-17 FSR study. During these flights, 1553 bus flight data was recorded capturing a multitude of weight and flight profile information.

During IGW testing in 2013, the author of this study was asked to provide fuel estimates to Laguna Army Airfield during the conduct of this testing. The test team hosted two C-17 aircraft over 14 days, each of which were performing 2-3 air drop missions per day and were required to refuel aircraft to over 400,000 lb. gross aircraft weight prior to each flight. The only model available to estimate fuel requirements was the legacy U.S. Air Force model described in Air Force Pamphlet (AFPAM) 10-1403 (app A, ref 6). Although this document described fuel consumption estimates for a wide array of flight conditions, the estimates are based off full flight conditions at higher speeds and higher altitude conditions. The author of this study came to understand that any estimate calculated by this reference would be grossly different from that of a personnel airdrop environment, which utilizes low speeds and low altitude conditions. As a result of being unable to provide an accurate estimate to the hosting airfield, the fuel resources were completely used up by the fourth day of testing. This caused a temporary suspension of flights in and out of the airfield until the fuel resources could be replaced. Cost and schedule for many projects were effected as a result.


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b. Advantages to User Community

When C-17 aircrews and mission commanders plan for their tactical mission requirements, both force and material projections are crucial. An expeditionary airborne force must not only be able to execute the mission, they must also have the logistical resources available for the both mission at hand, as well as any follow on missions required. The motivation for this study is to provide the U.S. Army Airborne Community and the U.S. Air Force with a simple model to be used by flight crews and mission planners that has been validated with empirical flight data.

The study contained within this test report addresses fuel consumption factor estimations for the FSR project and includes a wider range of gross weight changes, as well as varying atmospheric and temperature conditions. Empirical flight data is provided in the Excel file entitled “FUDGE_2.0_Data.xlsx”. This file provides all the empirical data and analysis conducted for this effort. This updated population of data is leveraged in a follow on study to update and calibrate the original model presented in this study. A second Microsoft Excel file entitled “FUDGE_Tool_Versions 1 and 2.xlsx” contains a working simulation and user interface of versions 1 and 2 of the FUDGE model. 1.4 PROBLEM STATEMENT, OBJECTIVES AND MODELING METHODOLOGY The primary questions being examined by this study are:

• What are the most significant variables affecting fuel consumption for a C-17 aircraft during a personnel mass exit?

• How much fuel is required to perform a mass exit airdrop insertion with the C-17A aircraft that weighs approximately 370,000-425,000 lb. gross weight at the time of green light (Time on Target- or first jumper out of the aircraft)? What is the quantity of fuel required to return to base?

• What is the cost, in U.S. dollars, of the fuel required for the mission? The primary test objectives of this study are:

• Determine which factors significantly affect fuel requirements and gross aircraft weight • Design a set of equations in a parametric model based on analogous historical flight

models, as well as empirical flight data collected within the last year. Make the model use factors that are simple to understand and readily available to the model user.

• Validate the model using statistical hypothesis testing and several other numerical testing methods

• Provide a working example of the model in a typical mass exit airdrop environment • Make conclusions and recommendations on the model, as well as recommendations for

future improvements


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Modeling Use Methodology: The FUDGE 2.0 model is based on version 1.0 and is intended to be used primarily for airdrop mission planners, aircrews and logistics professionals that require accurate projections of fuel resources. The functional flow chart below in Figure 1.4-1 shows the model use process for FUDGE 1.0, which remains unchanged for the second version.

Figure 1.4–1. FUDGE 1.0/2.0 Functional Flow Chart FUDGE is designed to take basic inputs about the mission and present timely and useful measures of mission resource and financial cost.

User%Receives%Air%Drop%Mission

Flight%Profile%Variables%input%to%

FUDGE%1.0

FUDGE%1.0%processes%calculations%

FUDGE%1.0%reports%model%

values

User%uses%model%to%project%

mission%fuel%resource%

requirements

FUDGE%Functional%FlowE1st%Level

1.0 2.0 3.0 4.0 5.0

Number%of%Flight%Legs

Air%Speed%for%Each%leg

FUDGE%Functional%FlowE2nd%Level

2.1

Distance%for%Each%leg

Aircraft%Gross%Weight

Total%Flight%Time%each%leg

Parachutists%Variables

2.2

2.3 2.4

2.5 2.6

Quantity%of%Fuel%Required%

(lb.)

Cost%of%Fuel%Load%($%US%

DoD)

4.1

Quantity%of%Fuel%Required%(US%gal.E%corrected%for%temperature)

4.2

4.3

Number%of%Aircraft Temperature

2.7 2.8


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1.5 CONCLUSIONS

! ! This fuel consumption study and the resulting FUDGE 2.0 model highlight which factors commonly used in the aviation and airdrop communities are accurate predictors of fuel needs at re-fueling airfields for C-17 aircraft. FUDGE 2.0 is a significant improvement on version 1.0 in terms of simplicity and accuracy. The model builds on cost drivers from the original study such as mission time and accounts for slower flight speeds seen in airdrop missions, which are vast improvements on currently used calculations. This parametric model can be continuously calibrated, updated and validated as aircraft flight data is captured during both testing and operational flights, as well as be compared to other fuel consumption models used in the private and defense industries. After conducting an update on model validation and statistical hypothesis testing, there is sufficient evidence that the currently used fuel consumption model published in the AF-PAM 10-1043 and FUDGE 1.0 produces over estimates of the fuel required for a mass exit personnel airdrop mission for the C-17. The new form of the model is presented in this study that more accurately predicts fuel consumption requirements for a mass exit mission. The author of this study recommends continued usage and calibration of the effort multiplier for parachutists’ weight. Also, the legacy model should continue to be used in order to plan transit to and from drop zones where the aircraft is being deployed over large distance. The results of the analysis for GWmt in this study indicate that the mean fuel consumption rate for the C-17 during a personnel airdrop mission is approximately 3,301 lb. /hour during a personnel mass exit mission, confirming the original assertion by FUDGE version 1.0 that the USAF Legacy model is overestimating fuel consumption for personnel air drop missions. Through an analysis of correlation, linear regression and simulation, the author of this study presents a linear equation to calculate gross weight change as a function of mission time. The linear equation correlates strongly with actual fuel consumption values in the validation set used to calibrate the model. More empirical data from airdrop missions is necessary to investigate and improve the FUDGE model. Threats to the model’s validity are included in Section 2.3, Model Assumptions and Biases. 1.6 RECOMMENDATIONS AND FUTURE IMPROVEMENTS a. Recommendations The author of this study recommends continued use of FUDGE 2.0 in a developmental airdrop test setting, as well as future calibration with empirical flight data collection. Additional data sets will allow the model to be further calibrated, analyzed and validated. It is recommended that flight data continue to be collected during a wide range of airdrop missions (including personnel and cargo air drop) with the 1553 data bus (or other instrumentation), so that the model can be further calibrated to suit the needs of varying mission profile requirements. Various types of cargo and high altitude personnel missions can be studied and developed for analysis.


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b. Future Improvements to Model There are several future improvements that the author will explore to improve the accuracy and functionality of this model: 1. Develop a Graphical User Interface (GUI) of the Model in a complex mathematical computing program, such as MatLab. GUI will include easy to input flight data values, unit conversion, and useful graphics for post model run data analysis. The test team will explore products that can be printed or saved to a .pdf or .jpeg file such as mission profile graphs and fuel consumption charts over time. 2. Partner with USAF AMC Test and Evaluation to develop a long term study of operational C-17 aircraft fuel resources, utilizing lessons learned both in this study as well as in the Iraq and Afghanistan wars. 3. Investigate and model additional cost drivers such as weather, loiter time, taxi time, time spent on ground and other logistical factors. Conduct a follow on study to examine other measureable factors that affect fuel requirements. Build equations into model and validate with empirical flight data. 4. Investigate other types of flight and airdrop profiles, such as cargo and high altitude precision airdrop. Calibrate model for use in these areas. Include multiple and varying flight legs into each mission, including transit to another airfield and refueling from airborne tankers. 5. Continue to calibrate the EMpax effort multiplier through empirical data collection during future mass exit operations. Determine whether the effort multiplier causes the data sets to be from different distributions, or if it can be removed from the model. End state: The author is dedicated to continuously updating and improving this model, as well as lessons learned from the C-17 IGW/FSR test program. Data collected from this study will be available for a wide variety of studies across the DoD.

SECTION 2. FUEL CONSUMPTION VERSION 2

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2.1 FACTORS AFFECTING FUEL CONSUMPTION The first step in the model development process was to understand what factors drive fuel consumption for a C-17. As this model is in its second version, only factors that significantly affect fuel consumption would be modeled and validated. Future improvements of this model will include analysis of additional factors to improve prediction accuracy. An initial product break down structure, as shown in Figure 2.1-1, was created to aid in isolating the most important variables for FUDGE.

Figure 2.1-1. FUDGE 2.0 Product Breakdown Structure for Fuel Consumption Factors

The next step in this process was to consult published references to determine as many possible factors affecting fuel consumption as possible. Resources consulted include Air Force Pamphlet 10-1403 (app B, ref 6) as well as several other published fuel consumption studies (app A, ref 5 through 10). The factors considered from this research are included in Table 2.1-1.


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Table 2.1-1. C-17 Fuel Consumption Factors Cost Driver Investigated in Model Type of Variable

Quantity of Fuel Needed for Mission Yes Dependent

Cost of Fuel Needed for Mission Yes Dependent

Number of Aircraft Yes Independent Distance Flown Yes Independent

Take Off Flight Profile Yes Independent Aircraft Gross Weight Yes Independent Landing Flight Profile Yes Independent

Aircraft True Air Speed Yes Independent

Meteorological Conditions

Held Constant (theoretical calculation

included to compensate for temperature affecting

fuel quantity)

Independent

Flight Altitude Assumed as a function

of Overall Mission profile Independent

Fuel Consumption Rates Yes Independent Price of Jet Fuel Yes Independent

Overall Mission Profile Yes Independent

Flap Settings Assumed as a function

of Speed, GW and Distance Traveled

Independent

Power Settings Assumed as a function


Independent

Time on Station Assumed as a function


Independent

Time on Ground/Taxi Time No Independent Cargo/Personnel

Requirements Use Empirical Values Independent

Mission Type (personnel, cargo etc.)

Standard Personnel Mass Exit Only for First

Iteration of Model Independent

Fuel Flow Rate

Derived from Change in Gross Weight, Mission

Time and Distance Flown

Independent

Total Fuel Taken on Board Yes Independent Refueling Destination

Altitude No Independent

Refueling Type (tanker, ground)

No Independent

The intent of this list was not to create an all-inclusive list for fuel consumption factors, rather to list as many significant variables that appear to have an effect on fuel consumption and


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then focus the list on a few vital variables that can be measured with empirical flight data collected during the C-17 IGW test program. Then, the list of factors can be narrowed and equations for predicting cost drivers can be determined. This was conducted by taking a data set of 143 individual airdrop profiles that occurred during 17 long duration air drop missions flown during the C-17 FSR project April 2014. The data is shown in app B, table B-1.


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2.2 MODEL DEVELOPMENT AND DEFINITION OF TERMS The data from Table B-1 was then divided into two sets, one for training the model, and one for validation of the model. The training data set was used only to understand fuel consumption factor relationship and to develop the model equations. The validation data set was then used to validate the model that showed the most promise (see section 2.5) using linear regression and correlation relationships. The data sets were chosen randomly, using the Randomize function in the Stat Plus tool pack for Excel 2013. Tables B-2 and B-3 in Appendix B show the test points randomly selected for each set.

As one would expect, flight operations are complex operations and therefore require a high number of variables to be examined. Because the unique project requirements of the C-17 FSR project dictate that a certain aircraft gross weight and mission profile be conducted, this study focuses on the few vital factors that affect fuel consumption as a function of the change in aircraft weight, speed, distance and mission time. In order to narrow the study to focus on the most impactful variables, a Pearson Correlation, standard regression and hypothesis testing with ANOVA (Analysis of Variance) analysis was performed in Microsoft Excel 2013 for Mac, with the Stat Plus tool package add-on software. The FUDGE 1.0 model (known as candidate 3 in the previous study) was brought forward unchanged to compare to the legacy and the updated FUDGE 2.0 and GWmt (Gross Weight change as a function of mission time) versions of the model.

The Pearson Correlation method is used to determine whether two variables move together. The method shows whether large values of one variable are associated with large values of others (positive correlation), whether small values of one variable are associated with large values of other the other (negative correlation), or whether values in both variables are unrelated (correlation is near zero). The primary output of the method is the R-Value, which is on a rating scale of -1 to 1. A strongly correlated pair of variables will have an R-value of close to 1 or -1. R-Values close to zero have little correlation. From the R-value, the R-squared value can be computed, which is defined as the estimate of the proportion of the variance explained by the pattern of association of the two variables.

Using these statistical tools, the Stat Plus tool package was used to compute the Pearson Correlation of the training data set from Table B-2. The results from the analysis are shown below in Figure 2.2-1.


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Figure 2.2-1. Training Data Set Correlation Analysis

From the correlation analysis shown above, it is apparent that the following factors have strong correlation. It is also possible to further refine the most significant variables by keeping the factors that have the highest individual R-Value in the Variable vs. Variable analysis. These factors are shown below in Figure 2.2-2.

Figure 2.2-2. Factors to Keep for Further Investigation

From this analysis, it can be seen that there are several factors in the empirical flight data captured during C-17 IGW have strong correlations above 0.5, and are positively correlated. It can also be seen that several factors have a little relevance, such as calibrated air speed. These variables were then used to develop two more candidate models to compute fuel quantity required (Qty), as well as analyze the legacy model. Qty is the primary output of the FUDGE model and is defined as the predicted amount of fuel in pounds or gallons that will be consumed during a personnel mass exit operation.


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The currently used (status quo or legacy) calculation, described in AF PAM 10-1043, used to estimate the amount of fuel required is given below:

USAF Legacy model: Quantity of Fuel Expended (lb.) = [(Distance/TAS) x (Fuel Flow)] – (Total Fuel) + (Destination Reserves) Where:

• Distance = total distance from takeoff to landing (nautical miles) • TAS = average airspeed (knots) -uses standard tables to compute average cruise speed for

different legs) • Fuel Flow = fuel burn rate in lbs. /hr. • Total Fuel = total fuel on board at takeoff (lb.) • Destination Reserve = required fuel reserves at destination (lb.)

Although this formula is easy to understand and compute, it uses assumed values for speed and distance (among other factors) that do not take into consideration the fuel demands for a specific mission type. The user of this formula must utilize factors located in tables within AF PAM 10-1043, which are mostly based on continuous long-range flights at high altitude and speeds, and not on conducting low-speed/low altitude personnel airdrop missions.

Candidate 3: Qty=Predicted Quantity of Fuel to be Consumed (lb.) = [Total Distance/Mean CAS]*[(((GW take off-GW green light)*2)-(#PAX*Median PAX Wt))/Total Flight Time] Note: Candidate 3 is the naming convention used in FUDGE 1.0 and is carried over to this study for ease of historical referencing. Where:

• Distance = total distance from takeoff to landing (nautical miles) • Mean CAS = average calibrated airspeed (knots) from takeoff to landing • GW Take Off = The Total Gross Aircraft Weight at time of takeoff (lb.) • GW Green Light = The projected Total Gross Aircraft Weight at time of landing (lb.) • #PAX = Number of parachutists to be deployed • Median PAX Wt = The mean parachutists total rigged weight (lb.) for the mission based

on historical data (see next section for further analysis) Candidate 3 was the leading candidate from the study conducted for FUDGE 1.0 and is

brought forward for this study for update and comparison to a new model.

Candidate Model 4: FUDGE 2.0 Gross Weight Calculator


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It is the goal of this study to develop a set of calculations that accounts for a specific mission as a function of the change in gross weight, distance and speed for a specific mass exit mission. FUDGE 2.0 purposely ignores the destination reserve calculation in order to focus solely on the aircraft fuel needs rather than take into account any required reserves. The logistics planner using published procedures will be able to calculate reserves separately. By basing the calculation on the change in gross aircraft weight, the user (mission or aircraft commander) can obtain more accurate fuel consumption estimates that are also necessary to account for weight and balance for the aircraft. Therefore, the second candidate model for Qty is given by:

Candidate 4 (FUDGE 2.0): Qty=Predicted Quantity of Fuel to be Consumed (lb.) = ([Total Distance Flown/Mean CAS]*[GWmt - #PAX*Median PAX Wt*EMpax])/ [Total Mission Time] Note: Candidate 4 is the naming convention used in FUDGE 1.0 and is carried over to this study for ease of historical referencing. Where:

• Distance = total distance from takeoff to landing (nautical miles) • Mean CAS = average calibrated airspeed (knots) from takeoff to landing • GWmt= Gross Weight as a function of mission time (lb.) • #PAX = Number of parachutists to be deployed • Median PAX Wt = The mean parachutists total rigged weight (lb.) for the mission based

on historical data (see next section for further analysis) • EMpax = Effort multiplier for parachutists’ weight based on historical data (see below for

analysis) • Total Mission Time = Total projected flight time in hours for the mission (hours. Decimal

hours format) Candidate 5: Qty=GWmt=Predicted Quantity of Fuel to be Consumed (lb.) = [(16961*Total Mission Time) +7080.9]* *see linear regression analysis below for explanation of slope and intercept for this equation) Where:

• Total Mission Time = Total projected flight time in hours for the mission (hours. Decimal hours format)

The notation for the above equations is purposely given in an Excel function language for

ease of placement in Excel worksheets. Currently, when aircrews and airdrop mission planners calculate weight and balance of the aircraft for a mass exit mission, a median jumper weight value is assumed. This median value is typically obtained by the airdrop commander giving a


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value to the pilot of the aircraft. Historical data shows that there is a wide variance between weights of individual jumpers on the same aircraft, and there are several different types of mass exit airdrop missions that may be performed (ones which the jumpers’ weights are drastically different). For example, some mass exit missions do not require the jumpers to wear combat equipment (ruck sack, weapon). In contrast, tactical missions require jumpers to be heavily loaded with all their basic combat load (rucksacks, ammunition, weapons etc.). To account for this difference, a linear regression relationship was computed for relationships between the mean jumpers weights obtained from the C-17 IGW project. These weights as shown below in Figure 2.2-3

Figure 2.2-3. Pax Weight Effort Multiplier Calculations

As can be seen from the analysis above, the median jumper weight for the C-17 IGW data was 295 lb. total rigged (total rigged is the individual jumpers total weight including body weight, all equipment, main parachute and reserve). This becomes the nominal value for jumper weight. Using linear regression, the deviation in jumper weight on both sides of nominal is +/- 0.2. Therefore, for the FUDGE 1.0 model uses the median weight of 295 lb. for the nominal case, which is a training jump with combat equipment. It can then be concluded that the effort multipliers for other types of jumps based on the analysis above are:

Table 2.2-1. PAX Weight Effort Multiplier

Type of Airdrop Mission EMpax Median Weight Value

(lb.) Training Jump (Administrative,

Non-Tactical) 0.8 -

Training with Combat Equipment 1.0 295 lb. Tactical (Operational) Mission 1.2 -

The effort multiplier for EMpax is incorporated into the FUDGE model because it is a useful parameter for both this study, as well as computing Computer Aided Release Points


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(CARP), as described in Air Force Instruction (AFI)-11-231. Continued calibration of this cost driver in future data collection efforts will help improve FUDGE as well as other studies that involve airdrop of personnel.

The next step of the study was to look at ways to simplify FUDGE 1.0 based on the most significant relationships from the correlation analysis shown above from the training data set. To do this a linear regression was performed to explore the relationships between gross weight change and total mission time. The graphical results are shown below in Figure 2.2-4.

Figure 2.2-4. Linear Regression Results from Training Set

This linear equation displayed in in Figure 2.2-4 is the basis for the GWmt calculation. It shows that the total mission time and gross weight change strongly correlate. As a result of this very strong correlation, it may be possible to simply use this linear equation and disregard all other variables. This hypothesis is tested below in Section 2.5. A regression comparison from for the recorded gross weight change from the training set versus the GWmt variable is shown in Figure 2.2-5.


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Figure 2.2-5. Linear Regression Results from Training Set for GWmt

As can be seen from the correlation and regression analysis, the GWmt model has the highest R and R-squared value when compared to the other factors affecting fuel consumption. Therefore, Qty and the remaining calculations can accurately calculated based solely on mission time using a linear equation relationship.

Now that the GWmt model was chosen to calculate Qty, the following variables, with their corresponding definitions and units for FUDGE were update and defined below in Table 2.2-2. The GWmt definition is highlighted in the table to denote the addition of this variable for this version of the FUDGE study, as it is an update to FUDGE 1.0.


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Table 2.2-2. Updated Fuel Consumption Study Definitions and Terms Symbol Definition Units

Qty Projected Quantity of fuel in pounds to be expended during mission for a single C-17 pounds

Qty gal Projected Quantity of fuel in gallons to be expended during mission, corrected for temperature and density for a single C-17 US Gallons

Qty ac Projected Quantity of fuel in pounds to be expended during a mission involving multiple C-17 aircraft pounds

Qty ac gal Projected Quantity of fuel in gallons to be expended during a mission involving multiple C-17 aircraft US Gallons

C Cost of fuel to be expended $U.S. (DoD Rates)1

D total distance from takeoff to landing nautical miles Mean CAS average calibrated airspeed from takeoff to landing knots GWtake off The Total Gross Aircraft Weight at time of takeoff pounds

GWgreenlight The desired Total Gross Aircraft Weight at time of first jumper release pounds GWmt Gross Weight as a linear function of total expected mission time pounds #PAX Number of parachutists to be deployed number

Median PAX Wt

The mean parachutists total rigged weight for the mission based on historical data (295 lb. for nominal) pounds

EMpax Effort multiplier for parachutists weight based on historical data (Section 2.2) number

T Total projected flight time in hours for the mission Hours 1 DoD Fuel Rates utilized for this study are derived from Defense Logistics Agency 2013 Fuel Contracts Report (app A, ref 11)

It is important to note the significance of reporting quantity of fuel required in both weight and volume units. Aviators must have accurate fuel estimates in these measurements so that the aircraft operated in its design flight performance envelope. Of primary concern is the weight and balance of the aircraft to meet a certain mission profile, which allows the aircraft commander to control fuel quantity between the many on-board fuel tanks, as well as position personnel or cargo appropriately on the aircraft. The aircraft commander must be able to manage weight and balance at all times so the aircraft center of gravity (CG) is always in balance. Weight of aviation fuel can vary up to 8% based on temperature. Therefore, all weight units given in this study are normalized to standard day sea level conditions for a temperature of 70-degrees Fahrenheit.

The conclusion after this analysis is that GWmt and Candidate 4 should continue to be explored in a simulation using the validation data set for analysis.


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2.3 MODEL BIASES AND ASSUMPTIONS There are several assumptions and biases in the updated FUDGE 2.0 and GWmt candidate models to include:

a. Fuel quantity and cost calculations generated by this study do not account for human labor or any other type of material resource. Future improvements to the model may be developed further to account for these factors.

b. The current version of this model does not account for any effort or material cost performed on the ground (i.e. taxi time, parking time, logistics factors)

c. Empirical Meteorological Data used to calibrate FUDGE is assumed to be in Standard Day Sea Level conditions. For instance, when flying at sea level under International Standard Atmosphere conditions (15°C, 1013 hPa, 0% humidity) calibrated airspeed is the same as equivalent airspeed (EAS) and true airspeed (TAS). If there is no wind, it is also the same as ground speed (GS). Under any other conditions, CAS may differ from the aircraft's TAS and GS. For version 2.0 of FUDGE, the effect of other atmospheric conditions, such as winds, are not accounted for. Air speed is computed in CAS to account for potential biases in meteorological conditions. Therefore, there may be some bias in the quantity of fuel being estimated, when using the empirical data collected from this study.

d. FUDGE 2.0 assumes a linear relationship for parachutist weight (PAX) using the effort multiplier EMpax discussed in Section 2.2. As missions vary, so will both the numbers and weight of parachutists and their accompanying equipment. It is assumed that all the jumpers on-board the aircraft will be deployed on one pass. GWmt ignores the EMpax variable completely.

e. The temperature input used to adjust for fuel volume is for the departure airfield only and based on industry accepted volume corrections. The updated models assume that the C-17 will be refueled on the ground only, not via an airborne tanker.

f. This study assumes that the gross weight of the aircraft at the time of first jumper exit is between 370,000 and 425,000 lb. gross aircraft weight. This range goes beyond the current allowable max gross weight for deploying parachutists from the C-17 (400,000 lb.).

g. The updated models assume that the empty aircraft weight for the C-17, as published by the manufacturer, is 282,500 lb. This is defined as the weight of the aircraft minus personnel, cargo and fuel.

h. The current version of FUDGE assumes that all aircraft will return to the same airfield after insertion of the airborne force, using the same flight profile.


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i. The limited amount of data points for this study (143 profiles over 17 total missions) may test the validity statistical significance of the model. More flight data is needed to improve assertions that certain variables do or do not effect fuel consumption.


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2.4 EXAMPLE USAGE OF MODEL An example solution for Qty based on GWmt is shown below using typical flight data inputs for an example mass exit operation: Problem: The airborne mission commander must insert three companies of airborne infantry into an objective in order to seize key terrain for follow on invasion forces. There will be three C-17 aircraft utilized for this mission and a total number of 306 parachutists deployed into the objective (102 per aircraft). The max allowable gross aircraft weight at the time of green light must be no more than 400,000 lb. for each aircraft. Other variables for the mission are provided below:

• Distance from airbase to release point = 100 nautical miles • Aircraft must return to the airbase after inserting jumpers • DoD Cost for a gallon of Jet Fuel is $3.62 per gallon (as of February 2015) • The C-17 commander determines that an average calibrated airspeed for the mission will

be 130 knots, for both the flight leg to the mission, the airdrop itself and the return • The current gross weight of each C-17 is 425,000 lb., including parachutists • The projected gross weight upon landing is 385,000 lb. • Since this is a tactical air drop mission, the jumpers are all fully combat equipped • Projected flight to the objective is 1.5 hours (due to mountainous terrain, the pilots must

maneuver carefully through mountainous valleys at lower speeds). • The air temperature at the air base is 60 degrees Fahrenheit.

Calculate the Quantity of fuel expected to be expended for the mission in terms of volume (gallons), weight (lb.) for both a single C-17 and the formation of three C-17. Calculate the cost in $US DoD Rates and correct the volume of fuel required for the conditions given.

1. Qty = ([16,961*1.5 hours] +7,080.9) =32,522.4 lb.

2. Qty gal =Qty*(1 gallon/6.7 lb. for Jet Fuel at 60 degrees F) =32,522.4 /6.7 =4,854.1 U.S. Gallons per C-17 3. Qty ac =Qty* 3 C-17 aircraft =32,522.4*3 =97,567.2 pounds for 3 C-17 5. Qty ac gal =Qty gal*3 C-17 aircraft =4,854.1*3

=14,562 U.S. Gallons for 3 C-17


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6. Cost (C) = Qty ac gal*$3.62 =14,562*3.62 =$52,714.44 total fuel cost for 3 C-17 aircraft This example shows the user that in order to conduct this mission, the re-fueling airfield must be able to supply a minimum of 97,567 pounds of Jet Fuel, or 14,562 gallons corrected for temperature, for 3 C-17 aircraft. The total cost of this fuel quantity is $52,714.44 using current DoD rates. The aircrew, mission commander and airfield logistics planner now have the required cost in terms of fuel quantity and funding that is required to execute the mission. Also, with this data, they can forecast ahead, based on mission requirements, how much fuel will be needed for follow on operations. Note: Temperature corrections for Jet A fuel are given by the following published international standards shown in Figure 2.4-1 (app A, ref 12):

Figure 2.4-1. Standard Specific Weight Conversions for Various Types of Fuel

FUDGE assumes the kerosene type jet fuel for its calculations because this is the most widely used jet fuel in the aviation industry.


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2.5 MODEL VALIDATION

In order to validate whether simply using the GWmt calculation was the closest model to actual values, a Monte Carlo simulation was executed using the Sim-Voi Monte Carlo simulation package plug-in for Excel Mac 2013. The main output of the simulation was to produce a Cumulative Distribution Function (CDF). The main objective of the Monte Carlo was to take each of the candidate model equations for Qty and run through a set of 10,000 simulation trials using the empirical flight data from the Validation Set in Table B-3.!

The!result!of!the!Monte!Carlo!is!a!plot!of!the!cumulative!probability!versus!the!value!of!Qty!for!each!trial!run,!for!each!candidate!model!as!shown!in!Figure!2.5-1.

Figure 2.5-1. CDF Curve Comparison for Updated Models

A closer examination of CDFs is shown in Figure 2.5-2.


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Figure 2.5-2. CDF Curve Comparison for Updated Models (Focused View)

The USAF legacy model equation is the legacy equation for predicting Qty, it serves as the baseline for the comparison for which the other candidate models are compared to. It is apparent that there is a significant difference between the GWmt function and the other simulations. It is also apparent that there may be little difference from candidates FUDGE 2.0, 1.0 and the legacy model in this simulation. However, none of the models are stochastically dominant over the others.!

In order to verify these assertions, further analysis on the data produced from the Monte Carlo simulation was conducted using statistical hypothesis testing. The appropriate statistical method for comparing two CDFs to each other is to utilize the Kolmogorov-Smirnov (ks) test and associated p-value. The ks and p-values for each CDF comparison were computed using the Sim-Voi statistics toolbox for Excel Mac 2013. The test statistic “ks” is the maximum absolute difference between CDFs at each measured value of x, and is given by the following equation.

!!" = max! |!1 ! − !2 ! |

The “ks” is a two-sample Kolmogorov-Smirnov test and is a non-parametric hypothesis

test. The null hypothesis in this case is that two samples of data are from the same continuous distribution, and the alternative is that the two samples of data are from different continuous distributions. Along with ks, the associated p-value was also computed, which is defined as the probability of observing a test statistic greater than “ks” assuming that the null hypothesis is true. A small p-value is evidence against the null hypothesis, while a small ks value is evidence to support the null hypothesis. The significance level used for this study is 0.05. Therefore, a p-value of less than 0.05 would indicate that the data sets being compared are from different continuous distributions, and therefore the null hypothesis should be rejected.


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Table 2.5–1 lists the “ks” and associated p-values for each comparison for this study.

Table 2.5–1. Statistical Hypothesis Testing Between CDF Outputs

FUDGE 1.0 vs. 2.0

FUDGE 1.0 vs. Legacy

FUDGE 2.0 vs. Legacy

GWmt vs.

Legacy GWmt

vs. FUDGE 1.0

GWmt vs.

FUDGE 2.0 ks -0.111 0.222 0.296 -0.630 -0.519 -0.593

p-value 0.994 0.466 0.153 0.000 0.001 0.000

From this analysis, the following conclusions are made:

a. There is sufficient evidence that GWmt is from a different distribution than the candidate distributions for the FUDGE 1.0 and 2.0 models. The null hypothesis that all candidate models come from the same distribution is rejected.

b. There is sufficient evidence that FUDGE 1.0, 2.0 and the legacy model are from the same distribution. The null hypothesis that these models are from the same distribution fails to be rejected.

c. It can be reasonably concluded that FUDGE 1.0, FUDGE 2.0 (candidate 4) and the USAF legacy model demonstrate distributions that are not consistent and may be overestimating actual required fuel quantities for C-17 mass exit operations.

Histograms of occurrences from the Monte Carlo Simulation for FUDGE 1.0 and 2.0 are shown in Figure 2.5-3.


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Figure 2.5-3. CDF Curve Comparison for Candidate Models

The histogram in Figure 2.5–3 shows where the majority of the Qty calculations occurred

in the Monte Carlo simulation. Finally, Analysis of Variance (ANOVA) was used to compare both candidates against the actual fuel values recorded during the empirical flight data collection in the validation set. Figure 2.5-4 shows the one-way ANOVA between each candidate and the actual fuel consumed during the C-17 IGW testing.


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Figure 2.5-4. ANOVA Comparison for Candidate Models

As can be seen by the ANOVA, the distribution for Qty for Candidates 2 and 3 are significantly similar, as evidenced by the low P-Values and the high F-values. The F and F-critical values test whether the ratio of the two variance estimates are significantly greater than 1. From the comparison of GWmt to the legacy and FUDGE 1.0 and 2.0 simulation outputs, it is shown that F is very high, while the P-values are low. The null-hypothesis that the means of the two distributions are significantly similar is rejected using ANOVA. A final direct comparison was made between fuel estimation model sand the actual fuel consumption values recorded in the validation set. Figures 2.5-5 and 2.5-6 show the direct


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comparison of model output values in a direct comparison to the actual fuel consumed using the validation data set.

Figure 2.5-5. Model Output Comparison Versus Actual Fuel Consumption Values

Figure 2.5-6. Model Output Comparison Versus Actual Fuel Consumption Values

In order to understand the mean and absolute error with each of the four models examined in this study, the error statistics were calculated as shown below in Table 2.5-2.


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Table 2.5–2. Mean Error Statistics for Candidate Models

Model

Mean Absolute Error (gal.)

Relative Error

Percent Error

USAF%Legacy 1,949% 0.267 27% Candidate%4 1,604% 0.203 20% FUDGE%1.0 1,927% 0.286 29%

FUDE%2.0%(GWmt) 764 0.178 18% The absolute error is defined as the magnitude of difference between the actual and the individual values of any quantity in question. In this study, it is clear that the FUDGE 2.0 model where fuel consumption as a linear function of gross weight change over time has the lowest error. The final conclusion from this validation analysis is that the Qty estimate for the GWmt model is not only from a different continuous distribution than the other candidates, but that the outputs are much closer to the actual fuel consumption values. Any mission planner can easily utilize the simplicity of the GWmt equation by only entering the mission time and a derived slope and intercept from empirical data. Lastly, according to Air Force Pamphlet 10-1403, the C-17 has a mean fuel consumption rate of 21,097 lb. /hour. The results of the analysis for GWmt in this study indicate that the mean fuel consumption rate for the C-17 during a personnel airdrop mission is approximately 3,301 lb. /hour during a personnel mass exit mission, confirming the original assertion by FUDGE version 1.0 that the USAF Legacy model is overestimating fuel consumption for personnel air drop missions. 2.6 FUEL CONSUMPTION MODELING TOOL The calculation for the most promising model (GWmt) concluded from this study has been automated in Excel (See “FUDGE_Tool_Versions 1 and 2.xlsx” provided). In this automated tool, the user supplies the following inputs (orange cells) for the planned mission. The green cells are the output calculations. Figure 2.6-1 shows an example mission in the FUDGE tool.


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Figure 2.6-1. FUDGE 2.0 Excel Based Tool (Worksheet 3)

The fourth worksheet, shown in Figure 2.6-2, in the FUDGE 2.0 GWmt calculator gives the user a quick reference to equations and definitions used in the model.


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Figure 2.6-2. FUDGE 2.0 GWmt Equations and Definition References (Worksheet 4)

APPENDIX A. REFERENCES

A-1

A. REFERENCES 1. “Systems Engineering Report For The C-17 Globemaster Max Gross Weight Study of the T-11 Personnel Parachute System.” Keith Allen, December 2013. 2. Memorandum For Vice Chief of Staff of the Army dated 23 February 2012, subject: Revalidation of C–17 Aircraft Airdrop Spacing and Aircraft Gross Weight during T–11 Parachute Operations. 3. Safety Release for Static Line Airborne Operations with the T–11 Personnel Parachute System in Support of the C–17 Globemaster III IGW Test, August 2013. 4. Draft Failure Definition Scoring Criteria, C–17 IGW and FSR Study, dated December 2012. 5. “Fuel Consumption and Operational Performance” Ryerson and Hansen, University of California at Berkley. Europe Air Traffic Management Research and Development Seminar (ATM2011). 6. Air Force Pamphlet (AFPAM) 10-1403 “Air Mobility Planning Factors.” Department of the Air Force, Air Mobility Command, 12 December 2011. 7. “Fuel Burn Estimation Using Real Track Data” Dano N. Chatterji, University of California at Santa Cruz, 11th AIAA Technology Integration Conference. 22 September 2011. 8. “A Methodology For Determining Aircraft Fuel Burn Using Air Traffic Control Radar Data,” Matthew Price Elliot, Georgia Institute of Technology, May 2011. 9. “Mathematically Modeling Aircraft Fuel Consumption, ”Pyatt, Coomes, National Center for Case Study Teaching in Science, Eastern Washington University, Cheney, WA, April 2009. 10. “Estimation of Aircraft Taxi-out Fuel Burn Using Flight Data Recorder Archives.” Khadilkar and Balakrishnan, Massachusetts Institute of Technology, 2009. 11. Defense Logistics Agency 2013 Fuel Contracts Report, DLA Energy Website: http://www.desc.dla.mil/DCM/DCMPage.asp?LinkID=DESCCutomerService 12. Aeronautical Vest Pocket Handbook, United Technologies, Pratt and Whitney Aircraft. 13. Fuel Delivery Gross Weight Estimator Version 1.0, K. Allen, University of Arizona SIE 564 Cost Estimation Final Project, July 2014. 14. Engineering Management Masters Project Deliverable #2 for the C-17 Globemaster Max Gross Weight and Reduced Formation Spacing Reduction Study of the T-11 Parachute System, K. Allen, December 2014.

APPENDIX B. ADDITIONAL DATA

B-1

B. ADDITIONAL DATA FIGURE'B)1.''FUDGE'2.0'Empirical'Data'Set'

Flight Number

Mean Calibrated Air Speed

(Knots)

Total Distance

Flown (nm) Total Mission Time

(min) Total Mission Time

(h.mm)

Total Gross Weight Change

(lb.)

Total Fuel Consumed

(gal.) Standard Day Sea

Level

Fuel Cost ($ Current DoD Rate)

1" 156" 450" 2:09:38" 2.16" 44520" 6,557" $23,735.26"2" 170" 123" 0:14:15" 0.24" 4480" 660" $2,388.45"3" 145" 487" 1:14:32" 1.24" 27280" 4,018" $14,543.98"4" 146" 456" 2:22:02" 2.37" 26880" 3,959" $14,330.72"5" 156" 489" 1:13:22" 1.22" 26600" 3,918" $14,181.44"6" 168" 509" 1:33:30" 1.51" 25280" 3,723" $13,477.70"7" 156" 350" 1:12:26" 1.21" 26600" 3,918" $14,181.44"8" 152" 450" 1:14:25" 1.25" 27320" 4,024" $14,565.30"9" 159" 340" 1:16:05" 1.26" 28120" 4,141" $14,991.81"10" 149" 560" 0:44:03" 0.44" 15400" 2,268" $8,210.31"11" 167" 349" 1:29:05" 1.49" 32080" 4,725" $17,103.03"12" 145" 423" 1:23:39" 1.39" 31080" 4,577" $16,569.90"13" 167" 239" 1:16:27" 1.27" 29480" 4,342" $15,716.88"14" 145" 198" 1:14:14" 1.23" 26400" 3,888" $14,074.82"15" 168" 501" 1:12:35" 1.21" 27480" 4,047" $14,650.60"16" 167" 376" 1:17:50" 1.29" 27480" 4,047" $14,650.60"17" 159" 369" 1:13:25" 1.22" 27080" 3,988" $14,437.35"

APPENDIX B. ADDITIONAL DATA

B-2

FUDGE'2.0'Empirical'Data'Training'Set'

Flight Number

Mean Calibrated Air Speed

(Knots)

Total Distance

Flown (nm)

Total Mission

Time (h.mm)

Total Gross Weight Change

(lb.)

Total Fuel Consumed

(gal.) Standard Day Sea

Level

Fuel Cost ($ Current DoD Rate)

GWmt Qty Candidate 4

lb.

Qty Candidate 3

(lb.) 1" 156" 450" 2.16" 44,520" 6,557" $23,735.26" 43,717" 59455"3" 145" 487" 1.24" 27,280" 4,018" $14,543.98" 28,113" 73890"8" 152" 450" 1.25" 27,320" 4,024" $14,565.30" 28,282" 64705"9" 159" 410" 1.26" 28,120" 4,141" $14,991.81" 28,452" 57548"10" 149" 230" 0.44" 15,400" 2,268" $8,210.31" 14,544" 54027"11" 167" 349" 1.49" 32,080" 4,725" $17,103.03" 32,353" 44994"13" 167" 349" 1.27" 29,480" 4,342" $15,716.88" 28,621" 48510"15" 168" 387" 1.21" 27,480" 4,047" $14,650.60" 27,604" 52316"

APPENDIX C. MODEL DEFINITIONS AND UNITS

C-1

C. MODEL DEFINITIONS AND UNITS

fudge 2.0_allen_sie909_final_revised 25 april

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