The interaction between the efficiency of the structural design and the cost of the structure used was studied. It is shown that future effort is best directed at producing a low cost structure of medium efficiency, but with the ability to withstand normal service wear. The trade-off between aerodynamic drag and structure weight in selecting a length to diameter ratio for the hull is evaluated along with the implications of power plan type and fuel cost on the economics of the airship. The choice of lifting gas is considered

Coughlin, S.

English

NASA Technical Reports Server

£5N76 1 022
° A STUDY OF DESIGN TRADE - OFFS !
USING A COMPUTER MODEL
Stephen Coughlin
C
,?
• ABSTRACT: The paper is an extension of previous work
_rt--_en by the author. It studies the interaction
between the efficiency of the structural design and the tt
cost of the structure used; and shows that future effort
--_' _ is best directed at producing a low cost structure of I
medium efficiency, but with the ability to withstand _
: _ normal service wear. The paper then goes on to study the
trade-off between aerodynamic drag and structure w_ight in "
selecting a length to diameter ratio for the hull, and -:to evaluate the implications cf power plan type and fuel
cost on the economics of the airship. As a final studythe choice of lifting gas is considered.
i
2
i
Ilcroduction
_he development of technological research into vehicles such as large
a_ _hips is in itself a complex problem. Whil. _ working on "new" "
, v_hicles of this type, the design engineer is unable to fall back upon
the benifits of past decelopment a:_d operational experience. This
means that those responsible for directing the cesearch effort have a)
• problem in separating tlmse areas of airship technology requiring
extensive effort from those that _an be. considered of little or no
importance.
In order to sur),_ountthis problem a cost model was developed at
Cranfield, which allowed us to study the impact of varying key design
: par_.meters. It permitted sensitivity analysis to be undertaken in
: order to produce a _imple ran_ing of problem areas.
* Research Officer, Cranfield Institute of Technology, Cranfield,
,;: England
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Oi
\ The results produced from the initial model were published in a
previous paper (ref I), a summary of which is given in table i.
J,
% change in operating
_: cost
4'
/ Parameter Initial Assumption -50% +50%
2 i Altitude 3,000 ft -4% +4%
L/D 6. -22% +22%
s.f.c .47 Ib/HP/hour -4% +7%
j s.w .5 ib/HP -1% +0%
, ¢
-'-_ mint e 06 inches -47% +70%
F 1.27 +108%
Transmission
efficiency .85 -10% +12%
• Max Speed/ ,
Cruise Speed I.i -5% +27%
Utilisation S,OOO hrs +55% -14%
Interest on
10% -15% +17%
Capital
Vehicle life iO years +46% -14%
Structure cost £20,OOO/ton -40% +42%
_'_ Gas cost _30/iOOO ft 3 -4% +3%
Power plant E20/HP -_% +_%
" cost
Fuel cost £20/ton -3% +5%
; Crew wages _140,OOO -4% +4%
Maintenance 4% first cost -9% +9%
Insurance 1% first cost -3% <2%
* Ratio taken as 1
TABLE 1
A SUMMARY OF THE SENSITIVITY ANALYSIS PRODUCED IN REF 1
Structure of the Model
The earlier model has now been improved in those areas shown eo be
critical in the prevlous study in order to pro¢ide greater cla,_t;,.
with the hope that it will show where future research would be best
directed. It must he stressed at this point that, although the
philosophy of the model is based upon a conventional design pr_cczs,
the result: produced here are intended to illustrate critical areas
and Key variables rather than suggest an ideal design.
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1976007927-077
_._ A simpllfied diagram of the model is shown in figure I. The model !
_ is structured to allow all the individual varlables to be varied
_ _ independently or jo.ntly, to cater for "trade-offs" to be studied.
il The input to the model, once it has been set-up, is the route capacity
in tons/year, range in miles and the flight altitude in feet. The ;i
speed is then determined for the lowest operating cost within the _
, constraints applied.
: _ SCALE FOR HULL FORM
I_ "_
MAKE WEIGHT ESTIMATE
a_-, '_ ESTIMATE SIZE
__k CALCULATE POWER REQUIREMENT
DESIGN SHELL
_ REESTIMATE ICEIGHT BREAKDOWN
_ ESTIMATE COST
IF NOT MINIMUM CHANGE SPEED
" IF MINIMUM
;. FIGURE 1 - MODEL STRUCTURE
¢,
Decision Criterion
The criterion chosen fo the evaluation was that of minimum fare
level for a set rate of return. This was chosen on the grounds that
a freight system is purely _.ommercial, social inputs being small,
and the ultimate decision would therefore be on commercial
possibilities.
Mqthod of Analysis Used
i'
As all parts of the system are as yet undefined, it was necessary to
conside_ it in a mathematical form, representing each component as _m
_ input to the operating cost The form of the mathematical model so
_ '
' A
1976007927-078
%,,'- , i
produced was then optimised for minimum operating cost as follows:
A technology assessment techniqu based upon Net Present Value
The net present value (NPV) of any project is given by
£=n
IqFV = _ (i - Co
t¢
£=1 !
i where
) £ is a year in the projects life
n is the life of the project
Cf is the net cash flow
Co is the first cost
r is the interest on capital
il _ If the cash flow is assumea smooth (ie there are no discrete
% payments all are smoothed throughout the project's life
' then the equation can be simplified to give1
-t
•i : r
Putting Cf = Cr - Cc
and Cr = T x F
where
Cr is the cash revenue/year
Cc is the cazh cost/year
T is the system capacity/year
and F is the charge per unit capacity/trip
gives -n]NPV = (TxF - Cc) [1 - r(1 + r) Co
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1976007927-079
?
)
as an optimum it can be taken that NPV = O, allowing the relationship
f
T - (I  r)
?
l
This now provides a simple relationship between the cost of a system _
in ter_s of its total first cost (C), its operating cost (C_) and its
fare level (F). (This Js easily modified for systems that h_ve
components with different book lives, but for simplicity in this
example, they have all been assumed constant).
_...-- Evaluation of CO and Cc
a) Considering the vehicle only;
The major first cost (Co) components are
" 1) Structure Cost
2) Lifting Gas Cost
3) Power Plant Cost
and the major annual cash costs (Cc) were assumed to be
4) Fuel
! 5) Crew Pay
: 6) .Repairs
' 7) Insurance
Table 1 sbows how these may be described in terms of vehicle
parameters
Function Of Major Parameters
_ Structure Cost Weight of structure W, u
_, Lift Gas Cost airship volume V
_" Power Plant Cost installed power S, u
i Fuel Cost fuel used S, u
i Crew Pay assumed constant
• Repairs ) assumed to be a [} CInsurance percentage of first cost o
• where W = size of airshio
_' u = speed of airship 1
_ V = volume of airship = f(W)
:: S = surface area of airship = f(W) _
< i
?
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1976007927-080
I? )
; Hence all components of the vehicle are some function, in this
simple case, of vehicle size and speed.
Analysis of Vehicle only
_ Using this theory and inserting the necessary engineering relation-
ships, it was possible to derive an iterative technique (fig I) that
gave a solution for the optimum design where
dF = O
du
The Datum Situation
; It is impossible in a paper like this to cover the full range of
_--" options available. For this reason a single specification has to be
chosen to act as the datum situation and, unless otherwise stated,
the assumptions should be taken as given in table 2.
The following is a list of the basic assumptions used in the
. assessment, together with the justification for these assumptions.
Assumption Value
Tons/year 150,0OO
• Range 1000 miles
Life 10 years
:, Operational altitude 5,OO0 ft
Length/diameter ratio 6.
: Specific fuel consumption .47 lb/hp/hr
Specific weight of power plant .5 lb/hp
Minimum practical value of t e .06"
Reserve fuel 33%
Power plant cost f20/HP
Fuel cost ilO0/ton
Crew wages I140,000
Maintenance cost 4% first cost
Insurance cost 1% first cost
Interest on capital 20%
TABLE ? ASSUMPTIONS USED IN STUDY
STRUCTURE
I As a first step in the study a totally uncon,_trained analysis was
) under:aken. Structures of w, rious efficiencies and ranges of costs
were studied, the results of which are shown in figure 2. The
structura _ efficiency is reflected by the equivalent shell thickness
@
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1976007927-081
_._,._ _, . _,, .,4. _ __-_,,_,__ _,,, .,'._ _ _
i .ZO
_. 50,000
.15
OPERATING iI40'OOO STRUCTURE
COST I/ COST £/TON
i/TON MILE /_30,OO0
.i0
' ._ i@
./)I/Xo,ooor
.O5 _0,OOO
f
zo Is io
' CRUISE SPEEDS - MILE_/HR
! .02 .O4 .O6 .O8 te - inches
, FIGURE Z UNCONSTRAINED SOLUTION
which is given by
te = Total Structure Weight x 12
, _ Density of Duraluminium x Surface Area
te .is in inches and other units in pounds and feet
_ From figure 2 it can be seen that in the unconstrained situation the
_i results produced are trivial. The low equivalent thickness would not
have any resistance to hail impact or bird strikes of the lowest
r magnitude. Those shells that do have higher equivalent thicknesses
are discounted by the low optimum cruise speeds associated with them,
which are incapable of providing an acceptable level of aerodynamic
stability.
The study was repeated with the solutions constrained to a minimum
: speed of 50 miles/hour and a minimum equivalent shell thickness of
.06 inches. This resulted in a set of solutions all of which lie
along one of the applied constraints. The results of this study are
shown in figure 3.
_, Analysis of figure _ shows a number of designs all above the .06
i: inch constraint, but with speeds of SO miles/hour. When these
! solutions were studi'_d in greater depth the structural efficiencies
_: which related to the designs were found to be so low as to make them
,; trivial solutions to the problem. This implies therefore that all the
useful solutions lie on the minimum equivalent thickness constraint
: had optimum speeds increasing from 50 miles/hour to 70 miles/hour.
_' The speed increased linearly Ps the structure was used more efficient-
ly from SO mile_/hour to some constant value, dependent upon the
structure cost assumed, the higher the structure cost the higher the
69
1976007927-082
• 20 12"
'_ .IS 09"
OPERATING
_ 08" te,, COST
E/TON MILE .IO .O7"
<
.06"
! .05 s,
4
1 2 3 4 S
' STRUCTURE COST £OOO/TON
FIGURE 3 CONSTRAINED SOLUTION
the steady state value of the optimum speed. The reason for this is
. , that for cost effectivness the more expensive structures have to be
used more efficiently. Hence, to off set the increased cost of the
structure the design becomes smaller and faster, as structure cost
increases. Figure 4 shows the value of these steady state re._ults
_', ' for optimum cruise speed.
z;
80
,' .Ol
te rain
70 .06
STEADY STATE
SPEED
MILES/HR 60
SO
1 2 3 4 S
STRUCTURE COST _OOO/TON
FIGURE 4 STEADY STATE SPEEDS
The Minimum Equivalent Thickness Constraint
From t},e results already l,roduced, it becomes apparent that the
equivalent thickness cohstraint is a key are_,. 'Fileproduction of ._
light weight design which is also resilient enough to withstand
70
#
J
i
1976007927-083
rigorous service conditions is difficult. Experience in structures
of this type is completely lacking and the possibility of achieving
a minimum value of .06" is unknown. A value of .i" has also been
considered, therefore, and the results are included in figures 3 and 4.
i Implications of the Structure Stud Z
: This study illustrates the unique problems of designing airship
structures. It shows quite clearly that high efficiency structures
have no major role to play in the shell design of conventional
airships, and the need is for practical scructures, the major
constraint being the ability of the structure to withstand general in-
service knocks. The future lies, therefore, in producing low cost
structures of medium efficiency, weight being a second order problem. , "
This lies in contradiction to present aircraft design philosophy,
where weight saving is a major criterion, and the use of materials ¢
such as titanium and carbon fibre reinforced structures is common-
_"" place Ia designing an airship shell there is a need for low density
structures, not to reduce weight but to allow greater thicknesses to
be used in order to increase resilience to damage. At the same time,
however, costs should be low whilst strength is a problem of the
second order. Structures that provide possible solutions to this
,- requirement are glass fibre structures or foam supported structures.
Thought must also be directed towards varying the design of the
conventional rigid airship in order to introduce some of the
requirements already outlined.
The same problems are also relevant to the production of the hull.
The structure should be robust enough to allow simple handling
during construction, since any special requirements will only
t _ increase production costs. This could lead to a situation where even
the simplest of structl,res could be highly expensive due to high
handling cost.
_ In conclusion to this section, it would seem that, with the relativly
: ': small variation in operating cost for changes in equivalent thickness
at the low structure costs, as shown in figure 3, a weight penalty
"' could be accepted provided the use of heavier structures as st in
,_ reducing production cost_. With this in mind, it is reco_ :,,ded that
_: future research should be directed at producing a struct : with a
il low equivalent thickness but with the major constraints o. being able
<-, to be easily and cheaply produced and to undergo normal handiing in
: service and during production.
t
LENGTH/DIAMETER RATIO
Closely related to the previous problem is the choice of length/
: diameter ratio of the hull. The selection of the optimum value
_' requires a trade-off between the structure weight and the skin
friction drag.
Dra_K
In order to relate the drag to the length/diameter ratio the follow-
ing drag relationship was used:
:_ Drag = q SD CD
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1976007927-084
1(, i
' where q is the dynamic pressure
• SD is the wetted drag area
r
and CD = .O3 1 + 1.S + 7 ,
-i77 = 7.Iz';. RE ",_" -"
' / (Source mef 2)
t
The results of this study are shown in figure 5.
.20 _ "
IOOC
_-" .15
_ OPERATING RANGE - MIEES
COST _____13OO
: . i/TON MILE .iO
3000
.05
t;
) _, _ =. . . a .,
0 2 4 6 8 10
; I/d
FIGURE S VARIATION OF LENGTH/DIAMETER
From this it can be seen that the optimum ratio Gf length to diameter
is 2.5, and that this value is independent of range. This optimal
value is based on a trade-off of fuel cost and structure cost and
. gives no consideration to stability. In selecting the final value it
will be necessary to consider the requirements of directional
stability, which is likely to increase the value.
FUEL AND POWER PLANT
Although it _as shown previously _Ref 1) that the choice of power
plant and the cost of the fuel were not critical areas in terms of
airship economics, it was decided that, with the rapid increase in
fuel prices that hos occured, the problem should be reassessed.
Fuel Cost
In order to study the effects of fuel cost on cost effectiveness, two
: designs were tindertaken to fulfill the same requirements. Each design
! had ,, different fuel cost; the first f20/TON, a typical value for two
_cars ago, and the second _lO,J'f(IN, a value representative of present
high fuel costs, the major characteristics of the designs are given
in table 3.
72
1976007927-085
|(
d
r
FUEL COST £20/TON flO0/TON
OPTIMUM MAX LIFT 1170 TONS 14_O TONS
OPTIMUM CRUISE SPEED 77 MILES/HR 51MILES/HR
OPERATING COST £,026/TON MILE £,O3/TON NILETABLE 3 EFFECT OF FUEL COST3.
'; _, The results illustrate how rapid changes in costs can modify past
)" results. Fuel cost has increased from a minor variable to a major
variable and has caused a marked decrease in the optimum speed ,¢
_' Power Plant Choice
,
The importance of the fuel cost is also reflected in a study of powerplant characteristics. The importance of specific fuel consumption is
..-." ._ clearly seen from figure 6, the specific weight of the power plant
having very little importance by comparison, (values of specific
weight from 5 to 5 fall on the same curve)
,, • •
os
, OPERATING
COST
E/TON MILE
,' ,04
.O3
i i • t • • ii | ii
1 2 3
SPECIFIC FUEL CONSUMPTION LB/ItP/LIR
FIGURE 6 EFFECT OF POWER PLANT
REFERENCES:
1. Coughlin S., An Appraisal of the Rigid Airship in the OK Freight
Market, Cranfiela-_TS Repor_ 3, Cranfield Institute of Technol6gy,-
_id. (March 1973).
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1976007927-086


A study of design trade (OFFS) using a computer model

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