J. ENG. DESIGN,
2000,
VOL. 11, NO. 3,
245 –263
Proposed measures for invention gain in engineering design
C . R E DE LI N G H UY S † *
Based on the phenomenon that invention manifests itself as at least one added or
removed or altered system parameter with respect to previous generations of the
system type, and that this parameter implies a positive differential value contribution with respect to the latter, a quantiŽed method for the measurement of
invention gain in design is proposed. Two types of assessment, one current and
the other retrospective, are proposed. The current assessment approach is useful
when choices between design concepts have to be made or when the creativity of
a number of competing design teams needs to be rated, while the retrospective
assessment approach produces invention gain histories for particular system
types. Application of the two methods is demonstrated by means of a Mini Baja
off-road racer design and the historic growth of aircraft useful load, respectively.
1. Notation
aymax
Maximum lateral acceleration
Ai
Inherent availability
c
Dimensionless value parameter
CD
Drag coefŽcient based on frontal area
G
Invention gain function
Lcirc
Length of racing circuit
m
Vehicle mass
MTBF Mean time between failure
Mean corrective maintenance time
Mct
n
Number of laps
N
Number of parameters
p
Parameter
S
Locating index
top
Operating time
ttot
Total time of event
V
Value
Vmax
Maximum speed
Vdc
Differential contribution to value
Vp
Isotechnology projection of value
Average speed
V
h
Transmission efŽciency
u
Transformed locating index
mymax
Effective lateral acceleration limit
Revision received May 2000
† Department of Mechanical Engineering, University of Cape Town, Cape Town, South Africa.
* To whom correspondence should be addressed.
Journal of Engineering Design
ISSN 0954-4828 print/ISSN 1466 –1387 online © 2000 Taylor & Francis Ltd
http://www.tandf.co.uk/journals
246
C. Redelinghuys
2. Introduction
In the present study, a quantiŽed parameter that would measure the inventive
contribution of a design is sought. As discussed in Redelinghuys (2000), various deŽnitions for design quality as are contained in the literature are inadequate for this
purpose as they could measure value due to design, but not added value due to
invention. The low creative component of routine design has to be ‘Žltered out’ Žrst,
before the value of true invention is exposed. Metrics allowing the measurement of
invention gain could be of value in:
(a) retrospective assessments of historical inventive contributions towards the
advancement of particular types of technical systems;
(b) current assessment of the invention gain contained in proposed, competing
design concepts;
(c) attempts at measuring the creativity of designers.
In this paper, a methodology for quantifying invention gain in design is put forward.
This relies heavily on the deŽnitions and conclusions of Redelinghuys (2000), of
which the following are repeated here for convenience (numbering has been
retained for ease of cross-referencing):
DeŽnition 5
The differential contribution is the difference between the achieved and the projected value
of a system designed to a speciŽed locating index.
DeŽnition 7
Necessary and sufŽcient criteria to judge if a design process could be classiŽed as an act of
invention are:
(a) The design is deemed as psychologically or historically original
(b) The design possesses a positive differential contribution
Necessary, but not sufŽcient criteria are:
(c) Creation of the design was not deducible from the current state of the art
(d) Contradictions had to be resolved during the process
(e) There were technological risks present
Corollary 2:
A necessary and sufŽcient criterion to judge whether the design of a TS is an invention is the
presence of at least one added or removed or altered system parameter, if such parameter(s)
causes a positive differential contribution, with respect to its TS(-1).
Presentation of the methodology for quantifying invention gain is followed by an
illustration of the present approach by means of two applications.
3. Quantifying invention gain
To Žnd a metric that could indicate invention gain is by no means an esoteric
task, as the success of numerous attempts at invention is judged ‘intuitively’ on a
regular basis. For example, on the Žrst day of testing, the Wright Flyer managed to
y a distance of 260 m in 59 s. After receiving the latter information, most people
would pass a verdict that the Wright Flyer as an invention was successful. Given any
one (or both) of the system parameters, i.e. distance of ight or time of ight, and
considering the potential utility of the device, a passing of judgement is possible. As
another example, the Hubble Space Telescope (HST) produces optical images with
a resolution of about 0.1 arc-s, which far exceeds that of ground-based telescopes,
Proposed measures for invention gain in engineering design
247
which are limited to a resolution of about 1.0 arc-s. In addition, the much publicized
dilemma due to the unexpected spherical aberations clearly indicates the presence
of technological design risks, and the fact that the designers could not have relied
on routine design methodology only. These factors might lead many in judging the
HST as a successful invention. However, such judgements are subjective and open
to criticism. From deŽnition 7(e), the presence of technological design risks is only
a necessary test for invention. Furthermore, seen from society’s point of view, for
example, there are those who would argue that the pictures which the HST produces
are of no beneŽt to a large fraction of the world population who live in poverty or
whose very existence is threatened by continued conict or anarchy (thus, the system
is valueless and does not qualify for originality). Perhaps the massive cost of
development and operation of the HST should rather have been spent, in some
inventive humanitarian way, towards the alleviation of the plight of the needy.
Another difŽculty that arises from superŽcial judgements of invention gain is their
absence of ‘calibration’, e.g. in aircraft design, how does the invention gain due to
the introduction of an all-metal construction compare with that of retractable
landing gear? The present approach towards the deŽnition of invention gain
attempts to circumvent some of these difŽculties. As will be shown, two assessments
of invention gain are proposed: one current, and the other retrospective. The major
features of the approach are succinctly introduced and, to demonstrate the method
more tangibly, examples are presented in the next section. It is proposed that in
order to evaluate the invention gain of a particular design, the following steps are
required.
Step 1. An assessor is needed. The assessor represents the interests of either the
investor, the producer (including the designer), the user/consumer or a sector of
society, or a combination of these parties.
Step 2. The ‘dimensions’ of an ‘invention metric space’ should be agreed upon
(at the onset of the design, for current assesssment). As a checklist for the identiŽcation of these dimensions, Žgure 1 of Redelinghuys (2000) or the application of
methods such as the use-value analysis (UVA) technique may be used. These dimensions imply the various system parameters that will be considered during assessment.
The parameters could be technical or commercial (or both), e.g. the ight distance
achieved or the Žnancial return on investment. By agreeing early on these dimensions for current assessments, potential difŽculties with the measurement of quality
are alleviated in cases where the design accomplished the addition or the removal
of a system parameter. For example, the Wright brothers had set, as the design goal,
a successful ight as a cardinal characteristic of their machine. An associated parameter such as time of ight from take-off to landing would thus be included as a
dimension of their invention space. Similarly, when Col. Shick was designing the Žrst
electric shaver Redelinghuys (2000), he had planned to produce a device that would
eliminate the need for water during the shaving process. Although the amount of
water needed as a system parameter might have been a valid dimension for earlier
razor blade designs, this dimension would not be considered when an assessor evaluated Col. Schick’s attempts.
Step 3. A suitable prototype of the attempted design of the technical system (TS)
should have been evaluated, and the results made available to the assessor. This
implies measurement of the achieved values for the various parameters that constitute the invention metric space. In the absence of a prototype, parameter estimation
should be based on an independent critical analysis of the design. For retrospective
248
C. Redelinghuys
assessments, historical records of the performance of the particular type of system
are needed.
Step 4. Subsets of the various parameters should be consolidated into value
parameters, preferably by means of mathematical relationships as expressed by a
value function V, which depends on N system parameters, pi, i = 1, N, and which is
usually expressed in the form:
V = V p1 , p 2 ,..., p N = V p
(1)
where p is the ‘solution state vector’ for a particular design solution.
Step 5. Such relationships could be established by means of theoretical and
empirical models, and the customer preference approach of Malen and Hancock
(1995a, b). Assume that the value parameter calculated, by whatever means, has a
magnitude of V.
Step 6. If V is a smaller-the-better parameter (e.g. speed to market), it has to be
changed into a larger-the-better parameter by means of a transformation such as
V ¢ = V0 – 1, where V0 is a reference threshold value.
V
Step 7. For current assessments, assuming that each V is of the larger-the-better
category, calculate for each such V four corresponding values, V(-1), VS, Vp and Vb,
where V(-1) is the value of the ‘closest’ existing TS of the same type, VS corresponds
with the state vector as given by the design speciŽcation, Vp is the projected system
value corresponding with the speciŽed locating index S and Vb corresponds with the
ideal physical limit for V. Examples of Vb are the Carnot efŽciency for a heat engine,
the speed of light, (transformed) zero production tolerance and (transformed) zero
production costs. With DV = V – V(–1), DVS = VS – V(–1), DVp = Vp – V(–1) and DVb =
Vb – V(–1), the following dimensionless value parameters are deŽned.
c=
V
Vp
Vp
=
Vs
V
Vs
cb =
Vb
Vp
Vp
=
Vs
Vb
Vs
and
Set c* = 1 and proceed to step 9.
Step 8. For retrospective assessments, historic performance data that spans at
least two prior generations are needed, e.g. in Žgure 1, V (again a larger-the-better
parameter) is shown as a function of the locating index S. Using the deŽnition of
variables as shown in the Žgure, the dimensionless value parameters are in this case
deŽned as:
Vdc
=
V dc (– 1)
c=
V – Vp
V(– 1) – V p (– 1)
and
cb =
0.
Vdcb
V dc (– 1)
In the event of DVdc(–1) = 0, the value parameters become unbounded. Set c* =
Proposed measures for invention gain in engineering design
Figure 1.
249
The history of a system value parameter.
Step 9. Invention gain is calculated as:
G=
cb – c* c
cb – c
=
`
0
if
c=0
1
if
c = 1 (current ) or if c = c b / ( c b + 1) (retrospective)
if
(2)
c = c b (both) or if V dc (– 1) = 0 (retrospective)
Step 10. DeŽning invention gain by means of equation (2) implies the following.
(a) For current comparisons, projected performance is not required due to the
relative nature of the assessement. G rises monotonically with the dimensionless value parameter c, from G = 0 for TS(-1) (for which c = 0) to G = 1
(for which c = 1) when the requirements of the development speciŽcation
are met. As c ® cb, G becomes extremely large.
(b) For retrospective comparisons, V and G are comparable with Altshuller’s
beneŽt and change in level of invention quantities, respectively, which are
shown in Žgure 2 (Altshuler, 1984). See (c).
(c) For retrospective comparisons, G also rises monotonically with the dimensionless value parameter c, from G = 0 for a zero differential contribution
(for which c = 0) to G = 1, for which c = cb/(cb + 1). As c ® cb (see (f)) or if
DVdc(–1) = 0 (in other words, a ‘Žrst time’ invention), G becomes extremely
large. By applying equation (2) to a technical system for which V grows sinusoidally with locating index (Žgure 3(a)) and for which the projected
250
C. Redelinghuys
Figure 2.
Altshuler’s (1984) (a) beneŽ t curve and (b) change in level of invention.
performance at any given locating index in its history is invariant, it is shown
in the Appendix that this system is being invented according to an invention
gain curve as shown in Žgure 3(b). This simple example demonstrates how
the present method ampliŽes breakthrough invention gain when the TS type
is in its infancy, and how invention gain dies out in its ‘old age’.
(d) For both current and retrospective considerations, G increases monotonically as the larger-the-better system parameter c is improved by adding a
positive differential contribution to TS(-1). From corollary 2, it hence follows
that G as deŽned by equation (2) is an indication of invention gain.
(e) The reason for having introduced the two assessments now becomes clear.
In situations where contemporary creative comparisons are called for, e.g.
Proposed measures for invention gain in engineering design
Figure 3.
251
(a) Elementary beneŽ t curve. (b) Invention gain for elementary beneŽt curve.
when a design team has to choose between various solution concepts, or if
the creative performance of a number of competing design teams is to be
compared, the current assessment approach should be applied. However, if
the value of a design effort is to be considered on a historic basis, the retrospective assessment is appropriate.
(f) An invention that is of such quantum magnitude that physical limits are
reached (c ® cb), would reect as G ® `.
(g) Equation (2) is a metric for invention gain and does not directly depend on
the effort that is required to effect the gain. Other factors that do inuence
252
C. Redelinghuys
a designer’s creative performance, such as level of expertise and the required
effort (expressed in person-years), are considered in Redelinghuys (1997a,
b).
4. Application: Mini-Baja design
As an example of the application of a current invention gain assessment, aspects
of the conceptual design of a Mini-Baja off-road racer are briey considered. The
Mini-Baja race is an annual inter-college competition that has recently been introduced to South Africa, and it provides a challenging student project that involves
the design, construction and testing of the racer. The rules of the competition
prescribe a one-person, four-wheeled conŽguration that has to be safe and powered
by a 6 kW lawnmower engine (see Žgure 4). During the competition, points are
awarded in various categories: (a) a static category, which covers the mechanical and
safety design and projected production costs; and (b) the performance category,
which consists of testing for acceleration, top speed, braking, skid pull, manoeuvrability, hill climb and endurance. As the rules clearly spell out how the individual
event scores are to be weighted and added to arrive at the Žnal score, postcompetition judgement of the quality of individual designs is a straight-forward
matter. As an illustration of the application of the present approach for gain of
invention evaluation, elements of a concept selection process during the conceptual
design phase are discussed later. As the competition has been running for many
years, especially in the USA, and many designs have been generated and tested, and
as the current student team whose design is being assessed has had little prior experience in this Želd, the nature of their design creation is most likely to be classed as
psychologically (rather than historically) original (Redelinghuys, 2000).
Figure 4.
Mini-Baja off-road racer.
Proposed measures for invention gain in engineering design
253
For the sake of illustration, the assessment will be restricted to the endurance
event only, for which the number of laps, n, which are completed in 3 h, is the crucial
performance parameter. In addition, a highly simpliŽed model for the calculation of
n will be used. Now, it is assumed that n depends on two other system parameters,
e.g. inherent availability, Ai, and average lap speed, V, where (Blanchard et al.,
1995):
Ai =
MTBF
MTBF + M ct
The total distance that the racer would cover is Ltot = Vtop. But according to the
deŽnition of Ai, top = Aittot. It hence follows that:
n = VA i t tot
L circ
The designer can inuence both V and Ai via the nature of the design solution
that is generated. In particular, Ai is determined by two system parameters, i.e.
MTBF, which is determined by the system reliability, and Mct, which depends on a
number of maintainability characteristics. V is determined by a host of parameters
such as vehicle mass (m), maximum speed (Vmax), transmission efŽciency (h),
maximum lateral (cornering) acceleration aymax and braking capability. It is
assumed, for an engine of given power and ignoring tyre rolling resistance, that Vmax
is established by the aerodynamic drag coefŽcient, CD, and that aymax is determined
by the effective maximum lateral friction force that the road can exert on the tyres.
This friction force is determined by the effective maximum friction coefŽcient, mymax ,
which is a function of the road surface type and the tyre and the suspension characteristics. In the following treatment, it will be assumed that Ai is not affected by the
proposed design variants. The larger-the-better value parameter V as was introduced in step 4 of the previous section is hence equated to V. Assuming that a functional relationship of the form of equation (1) can be found, the designer is in a
position to analyse the quality of various designs by means of computation. Towards
this end, a vehicle dynamics model that is capable of predicting V for a given racing
circuit was formulated and programmed. In this model, an ‘ideal’ driver is assumed,
i.e. a driver who would fully exploit the vehicle-inherent performance capability at
all times.
A Mini-Baja racer that participated in the previous competition was available to
serve as TS(-1) . Four new design concepts, variants 1–4, were proposed by the design
team. The major features of the design variants are summarized in table 1.
In order to perform the quality assessment, an ‘ideal’ vehicle has to be deŽned.
The various parameter values of the ideal vehicle should correspond with their
Design
Description
TS(-1)
Variant 1
Variant 2
Variant 3
Existing Mini-Baja design
Improvement of cornering capability via suspension modiŽcations
Reduction of aerodynamic resistance by means of fairing
Improvement of transmission efŽciency through the addition of
gears to the continuously variable transmission
Reduction of vehicle mass using aluminium instead of mild steel
Variant 4
Table 1.
Mini-Baja design variants.
254
C. Redelinghuys
Lateral friction coefŽcient
Drag coefŽcient
Transmission efŽciency
Mass (kg)
Table 2.
TS(-1)
1
2
3
4
Ideal
0.4
1.2
0.65
240
0.6
1.2
0.65
240
0.4
0.8
0.65
240
0.4
1.2
0.8
240
0.4
1.2
0.65
220
2.5
0.04
1
180
Parameter values for design variants.
respective extreme physical limits. Hence, for this vehicle, mymax = 2.5 was chosen, a
value that has been experimentally demonstrated for rubber acting on silicon
carbide (Dixon, 1996), and CD = 0.04, which has been achieved for streamlined cylinders (Katz, 1995). Parameter values for the various design concepts are shown in
table 2.
The environment in which the system is to function has to be described. For the
purpose of variant comparison, a simple horizontal racing circuit, consisting of two
circular arc segments connected by means of straight sections, was chosen. The radii
of the arc segments are 17.5 and 12.5 m, respectively, and their centre distance separation is 150 m. Simulations revealed that for TS(-1), the obtainable average speed
when driven around this circuit is 39·507 km h–1. The overall design goal was to
increase V to at least 45 km h–1. Figure 5 shows the attainable speed plotted on the
circuit for the ideal vehicle and for TS(-1). Figure 6 shows the increase in V that the
design variants achieve, as simulated on the computer. Calculating their corresponding design quality as an invention gain by means of equation (2) allows the
construction of Žgure 7, from which it follows that the design variants are to be rated,
considering the value of their respective gain in invention, in the following order: 1,
3, 2, 4. Making use of any one of the design concepts in isolation would not be
sufŽcient as G < 1 for each. However, simulations reveal that the combination of all
the variants into one design would result in G = 1.319, which would be adequate
(from a technical performance point of view) but probably too expensive (Žnancial
Figure 5.
Speed-on-circuit plot for TS(–1) and ideal vehicle.
Proposed measures for invention gain in engineering design
Figure 6.
Speed increase for Mini-Baja design variants.
Figure 7.
Invention gain for Mini-Baja design variants.
255
256
C. Redelinghuys
constraints would of course also be stated in the design speciŽcation). Finally, it is
pointed out that for the combined design, a linear addition of individual G values
gives G = 1.058, which implies an error of about 20% with respect to the value
obtained by means of a full non-linear simulation. This error is mostly due to the
non-linear transformation of equation (2), as a linear addition of DV causes an error
on V of only 4%.
5. Application: aircraft payload history
As an example of a retrospective assessment, the history of the payload (or
disposable load) capability of aircraft is briey analysed. The take-off weight of an
aircraft can be divided into the respective weights of the structure, the power plant,
the equipment and the disposable load (the latter consisting of fuel and passengers).
Before 1903, the sum of the Žrst three of these weights exceeded the possible takeoff weight as determined by the state-of-the-art, negating manned ight. Due to the
beneŽts of various inventions, structural and power plant efŽciencies improved,
permitting their relative weight contributions to decrease to a point that disposable
loads could be carried for reasonable distances. The success of the Wright Flyer was
also clearly dependent on the phylogeny law of invention (Dasgupta, 1996), which
states that the appearance of an invention relies on a linked network of mature artifacts or artifactual forms leading to the invention in question. For example, Renard
(1903) published a paper stating that the engine of a piloted airplane should not be
heavier than 17 pounds per horsepower. The engine used by the Wright brothers
was 15 pounds per horsepower (von Karman, 1954).
As Redelinghuys (2000) pointed out, there has been a steady growth in payload
capability of aircraft since the days of the Wright brothers. The useful load of the
Wright Flyer was about 68 kg (counting pilot Orville and just over 2 kg fuel) (Cleveland, 1970), while the world’s largest aircraft today, the Ukrainian Antonov An-225
Mriya, has a payload capability of 250 000 kg (Anonymous, annually). The basic
driving force toward larger aircraft has been the desire for lower total costs associated with moving goods and people, and for the ability to move them further (Cleveland, 1970). The direct operating cost of an aircraft, measured in cost per (mass 3
distance) of payload, decreases with an increase in design gross weight. The steady
growth in payload saliently reects the beneŽt of numerous inventions and contradictions that had to be resolved, in order to achieve the payload growth. One of the
more troublesome contradictions that the designer has to face when a scaling up of
aircraft size is attempted, is the square/cube law. When an object is scaled up,
preserving geometric similarity and structural characteristics, the object’s mass
grows in proportion with the cube of the linear dimension, while typical areas (such
as a wing area) grow proportionally to the square of the linear dimension. This
results in structural stresses and the wing loading (N m–2) growing proportionally to
the linear dimension, or proportionally to the cubic root of the mass (the
square/cube law). If design philosophy and technology had remained static through
the years, growth in aircraft size would have been halted by the square/cube law. In
order to Žght the growth in structural stresses with increasing aeroplane size, the
structure to payload mass fraction would have to be increased, which could only be
carried on up to a limiting point when the payload mass vanishes —a contradiction,
in the Altshuller sense. Adverse scaling laws, such as the square/cube law, are of
course not limited to aircraft design; they plague mechanical engineering designers
Proposed measures for invention gain in engineering design
Figure 8.
257
Wing loading of birds (von Karman, 1954).
whenever scaling up of technical systems (such as brakes and gears) is attempted, in
general. The square/cube law had already been identiŽed in the previous century,
e.g. von Helmholz (1873) applied it to ying birds. Von Karman (1954) generated
Žgure 8, on which the straight line represents the von Helmholz result. From these
considerations, it was concluded that there is a certain size beyond which a living
being is unable to y.
The square/cube law is by no means the only problem that has hampered
designers in search of yet bigger aircraft. Some of the other contradictions that
inherently inhibit size growth include the following (Cleveland, 1970).
•
•
•
•
•
•
•
•
Federal Aviation y-over noise limitations.
The airport interface, e.g. larger aircraft require thicker runways.
Increasing standards of reliability and safety.
Adverse aeroelastic effects such as the Žrst wing symmetric bending frequency
approaching the aircraft short period frequency.
Increased structural deections, generally inherent in larger aircraft, complicate the close control in gaps and slots in high lift devices.
Higher interior noise, requiring a disproportionate high allocation of soundprooŽng weight.
The increasing strength of the trailing vortex wake causing a hazard for following aircraft.
Increasing sluggishness of aircraft handling, due to a cube/Žfth power ‘law’
stating that the aerodynamic or driving moments that act during aircraft
manoeuvre are proportional to the third power of its dimensions, while the
inertial moments are proportional to the Žfth power. The sluggish response of
258
C. Redelinghuys
•
•
•
•
a large boat, compared with a small one at the same speed, is a familiar illustration of this powerful effect.
Substantial increases in the power required by the ight control systems of
larger aircraft.
Adverse weight increase of the propulsion unit due to its speciŽc weight
(engine weight/thrust) following the square/cube law.
Poorer engine response rates due to scaling up.
Manufacturing complications, such as limits of press capabilities for forgings
and limited aluminium sheet size.
In spite of all these problems, human inventiveness has resulted in aircraft useful
load fraction, expressed as the ratio of payload mass to gross mass, to actually
increase through the years. To illustrate, the solid line of Žgure 9 (Cleveland, 1970)
charts the historical growth of useful load fractions for 23 aircraft. For comparison,
square/cube law projections based on the then-existing state-of-the-art at nine
Figure 9.
Growth of aircraft load fraction (Cleveland, 1970).
Proposed measures for invention gain in engineering design
259
aircraft points are shown as dotted curves, the isotechnology lines that were referred
to in Redelinghuys (2000). Each one of these lines purports to portray what the
useful load fractions of larger or smaller variants would have been, if designed simultaneously with the actual aeroplane. The sources of invention that have allowed the
continuous divergences of Žgure 9 are manifold, and they could be grouped into four
areas (Cleveland, 1970).
(1) Structural, including materials, inventiveness, fasteners and analytical capabilities.
(2) Aerodynamic, including both lift and drag parameters, and both internal and
external ows.
(3) Propulsive, including fuels and systems as well as main engines.
(4) Systemic, including the host of subsytems providing ight control, secondary power, life support, and communication and navigation.
The information contained in Žgure 9 was used to perform a retrospective invention gain analysis by means of equation (2). The value parameter V was equated to
the useful load fraction, for which the ideal physical limit is, of course, Vb = 1. Nine
steps of invention gain were calculated, corresponding to the nine distinct aircraft
types shown in Žgure 9. For example, the calculated gain in invention for the Boeing
707 (aircraft G) would be with respect to the state-of-the-art of the Lockheed Constellation (aircraft F). In performing the calculations, extrapolations of Cleveland’s
Aircraft
Appearance History/morphology
A
Wright Flyer
1903
B
Curtiss JN-4H
1909
C
Junkers F-13A
1919
D
Douglas DC-3 Dakota
1935
E
Curtiss C-46 Commando 1942
F
Lockheed Constellation 1943
G
Boeing 707
1954
H
Boeing 747
1969
I
Lockheed C-5A Galaxy
1968
Table 3.
First sustained, powered ight: biplane, twin
pusher propellers, front biplane elevator,
front and rear rudders
First mail plane in the USA: biplane, single
pusher propeller, inherently stable, front
biplane elevator, large between-wing ailerons,
Žxed rear Žn and tail plane, tricycle landing
gear
Four-passenger transport: Žrst cantilever lowwing monoplane, single engine, Žrst all-metal
construction (1915)
Most successful airliner in history (21
passengers, 13 000 built): twin, wing-blended
engines, variable pitch propellers, monocoque
construction, wing aps, retractable landing
gear
Military transporter (30 paratroopers or 40
passengers)
51-passenger airliner: pressurized interior,
four engines, reversing propellers for ground
braking, triple tail Žn
219-passenger, high subsonic Mach number
airliner: high sweep-back wing, four turbojet
engines
442-passenger, (jumbo) wide body airliner:
four turbofan engines
Cargo transport (178 000 kg useful load)
Aircraft types considered.
260
C. Redelinghuys
Figure 10.
Invention gain for aircraft families.
projected curves sometimes had to be carried out, and the data could not be read with
a great accuracy from the graphs. The present calculations should hence be regarded
as approximate. Designations and brief historic and morphological descriptions
(Anonymous, annually; Gibbs-Smith, 1970; Jarrett, 1997) for the various aircraft are
shown in table 3.
The results are shown in figure 10. As the design of each one of the aircraft
resulted in a positive differential contribution with respect to its predecessor, each
would be classed as an invention, according to definition 7(b). The present mathematical approach allows these inventions to be quantified and compared, as
shown on the diagram. The invention gain for the Wright Flyer, being the first
invention of this type of system, is immeasurably large by equation (2), so it fills
the graph’s vertical scale. Two other aircraft, the Douglas DC-3 and the Boeing
707, stand out as being, from a structural efficiency point of view, historically
significant. Before these two aircraft are awarded substantial credit for being
exceptionally inventive designs, one should take cognisance of the fact that associated with each is a multitude of other co-existing and prior designs. Each one of
Proposed measures for invention gain in engineering design
261
the nine aircraft considered here is thus a representative of a family, and its
performance is the consequence of the cumulative knowledge gained from
developing a large number of aircraft.
Seeing the DC-3, thus, as a representative of the invention gains of the betweenworld-war era, its outstanding performance can be ascribed to many inventions, a
small number of which are listed in the Žnal column of table 3. In addition, piston
engine technology advanced with huge strides in this period. Quoting Cleveland
(1970): ‘In the period 1917 to 1945, the speciŽc weight of the piston engine decreased
from three to one lb/hp; engine power requirements increased by about 1200%; and
the speciŽc power was improved by about 400%. These accomplishments were made
possible as a result of improved antidetonation characteristics of fuel, higher r.p.m.
and piston speeds, and better breathing through use of larger valves, higher
compression and supercharging’.
A quantum jump in aircraft performance was experienced with the introduction
of the turbojet, weighing only one-quarter as much as the piston engine and cruising
with essentially the same efŽciency at 720 km h–1 and with progressively superior
efŽciency as speed increases. The high invention rating for the Boeing 707 is mainly
due to the turbojet.
6. Concluding remarks
Based on the criteria for the detection of invention as formulated in Redelinghuys (2000), a quantiŽed method for the assessment of gain in invention was
introduced. Two types of assessment, i.e. one current and the other retrospective,
were proposed. The current assessment method, which should be useful when
choices have to be made between proposed design concepts, or when the creative
performance of competing design teams is to be compared (Redelinghuys, 1997a,
b), is more or less similar to existing value analysis techniques. This is because the
‘zero offset’ due to routine design, which has to be subtracted from the system
achieved performance to leave the inventive contribution, becomes irrelevant when
the differences between current designs are evaluated. The essential difference
between the present approach and established value analysis is the transformation
from value parameter c to invention gain function G (equation (2)). The value parameter is deŽned such that system projected performance is not required for current
assessment, which simpliŽes calculations considerably.
The retrospective analysis of invention gain for a particular type of technical
system relies on utilizing data depicting the historic growth of a value parameter as
a function of a locating index for the system. For a series of locating index values, a
value function is calculated progressively by determining the ratio of the present to
the previous values of invention gain. This approach produces invention gain
histories that are similar in form to the popular impression of high invention level
for early, Žrst-time breakthroughs (at ‘system infancy’) and diminishing level of
invention towards system ‘old age’, e.g. see Žgures 2b, 3b and 10. The retrospective
assessment could be useful for the analysis of the historical growth of selected types
of technical systems, as was demonstrated by means of the aircraft application.
Evaluation of invention gain according to the present approach could be applied
when the patenting of an invention is considered. With due consideration of technical as well as commercial merit, such an exercise should assist in judging the proŽtability of new technologies.
262
C. Redelinghuys
References
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Appendix: retrospective analysis of elementary beneŽt curve
An elementary beneŽt curve (historic value V as a function of locating index S)
for a TS is deŽned as follows.
(a) By performing a simple origin shift and variable scaling on the curve, a transformed beneŽt curve of the following form is obtained:
V = 1 + sin u
–p /2 £ u £ p /2
where V is the transformed value parameter and u is the transformed
locating index (Žgure 3a).
(b) For any given u and Du, Vp(u + Du) = V(u), or the projected performance Vp
is invariant.
(c) For any given u, Vb ® `. This implies that equation (2) becomes G = c.
Proposed measures for invention gain in engineering design
263
Now, with the help of Žgure 1 and considering equal increments of locating
index, Du:
G=
Vdc
V dc (–
1)
=
V – V ( – 1)
sin ( ) – sin ( –
)
=
V (– 1) – V (– 2 ) sin ( –
) – sin ( – 2
)
Using equation (B1), Žgure 3b was constructed for Du = 0.0873 (5°).
(B1)