Unit 1 Exam Name _________________________
Math 331 VB
Spring 2015
DIRECTIONS: I grade on both the work AND the final answer, so show as much work as possible within
each question. This is the only way I can give partial credit if you happen to make a mistake. TI-89’s are wonderful
calculators, but they don’t show me if you know anything about calculus! Show all work on the exam itself, you should
not use any outside paper, notes, etc.
1) Calculate the limits of the following functions (use the given graph of the function f for part A and B).
-6
-4
-2
0
2
4
6
8
-6 -4 -2 0 2 4 6
a) (3 points)
2
lim
x
xf
b) (3 points)
1
lim
x
xf
c) (6 points)
289
17
lim
289x
x
x
d) (6 points)
2
2
9 2
lim
8 6x
x
x x
e) (6 points)
0
1 1
7 7
lim
x
x
x
2) (8 pts) Find the average rate of change for each function over the given interval.
a)
2 3y x x , between 2 and 3x x
b)
2 3y x x , between 2 and 2.5x x
c) Based on your answers to parts (a) and (b) estimate the instantaneous rate of change at x = 2.
3) (7 points) Verify the derivative of the function
9
1
( )
x
f x
at 4x is 1 , using either form of the definition of derivative
0
lim
h
f x h f x
h
OR
lim
x a
f x f a
x a
.
4) (7 points) Sketch the graph of the derivative for the function shown below, right next to it.
2
3
f x
2 4 6
-2
-2 -4 -6
x
5) (7 points) Write the equation of the tangent line to
2( ) 6 3f x x at x = 2.
6) (6 points each) Calculate the derivative of each of the following (use the shortcut rules from Chapter 4 and don’t worry about
simplifying too much):
a)
9 9( ) xf x x
b)
2
4
5
x x
g x
x
c)
3
2 4
( ) 8
3
h x x
x
d)
42
ln
( )
x
x
l x
e)
2 4 1( ) 3 xm x x e
7) (7 points) The height of an object after t seconds is given by 29 27 2tH t t .
Use calculus to determine the maximum height reached by the object.
8) (10 pts) An actuary has determined that in a certain population, the number of people surviving ( )P x , to age x years is given
by ( ) 400 101P x x .
a) Calculate (75)P and explain the meaning of this answer (or provide a label for the answer.)
b) Calculate '(75)P and explain the meaning of this answer (or provide a label for the answer.)
The iconic plane could fly from London to New York in just three
hours but was retired from service because it became unprofitable
A decade ago to the day, Concorde completed its last ever
commercial passenger flight.
Within the space of five minutes, three flights landed at Heathrow
Airport, br ...
Interactive Powerpoint_How to Master effective communication
Unit 1 Exam .docx
1. Unit 1 Exam
Name _________________________
Math 331 VB
Spring 2015
DIRECTIONS: I grade on both the work AND the final answer,
so show as much work as possible within
each question. This is the only way I can give partial credit if
you happen to make a mistake. TI-89’s are wonderful
calculators, but they don’t show me if you know anything about
calculus! Show all work on the exam itself, you should
not use any outside paper, notes, etc.
1) Calculate the limits of the following functions (use the given
graph of the function f for part A and B).
-6
-4
-2
0
2
2. 4
6
8
-6 -4 -2 0 2 4 6
2
lim
x
xf
1
lim
x
xf
c) (6 points)
289
17
lim
289x
4. x
2) (8 pts) Find the average rate of change for each function over
the given interval.
a)
b)
5. c) Based on your answers to parts (a) and (b) estimate the
instantaneous rate of change at x = 2.
3) (7 points) Verify the derivative of the function
9
1
( )
x
f x
derivative
0
lim
h
f x h f x
7. 4) (7 points) Sketch the graph of the derivative for the function
shown below, right next to it.
2
3
2 4 6
-2
-2 -4 -6
x
5) (7 points) Write the equation of the tangent line to
8. 6) (6 points each) Calculate the derivative of each of the
following (use the shortcut rules from Chapter 4 and don’t
worry about
simplifying too much):
a)
2
4
5
x x
g x
x
10. x
x
e)
7) (7 points) The height of an object after t seconds is given by
Use calculus to determine the maximum height reached by the
object.
11. 8) (10 pts) An actuary has determined that in a certain
population, the number of people surviving ( )P x , to age x
years is given
a) Calculate (75)P and explain the meaning of this answer (or
provide a label for the answer.)
b) Calculate '(75)P and explain the meaning of this answer (or
provide a label for the answer.)
The iconic plane could fly from London to New York in just
three
12. hours but was retired from service because it became
unprofitable
A decade ago to the day, Concorde completed its last ever
commercial passenger flight.
Within the space of five minutes, three flights landed at
Heathrow
Airport, bringing down the curtain on three decades of
supersonic
travel.
The final flight arrived from New York and as it touched down
at
16.05, thousand of onlookers were there to experience one of
the
most iconic moments in the history of aviation.
One hundred celebrities were on the final flight, including
actress
Joan Collins, who said there were “cheers and tears” among her
fellow passengers when the plane landed.
She was joined on board by model Jodie Kidd, broadcaster Sir
David
Frost and politician Tony Benn.
13. The iconic plane, which, with a top speed of around 1,330mph,
could
travel faster than the speed of sound, was retired by British
Airways
after 27 years in service because it was no longer profitable.
It also never recovered after a horrific crash near Paris' Charles
de
Gaulle airport in 2000, in which 113 people died.
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NEWS
EMMERDALE
News UK News British Airways
Concorde's final flight: A decade after the
aircraft last went supersonic we look back
at its illustrious history
Concorde's final flight: A decade after the aircraft last went
supersonic we look back at its illustrious h...
Some British Airways staff were angry that Concorde was being
retired, however the firm's chief executive officer Rod
Eddington said
at the time: "It's an old plane - it doesn't look it - but it was
designed
in the 50s and built in the 60s."
"It is a wonderful plane, an icon, but its time has come."
Concorde timeline
December 11, 1967: First prototype unveiled in Toulouse,
France
March 2, 1969: Concorde flies for the first time, from Toulouse
16. October 1, 1969: First supersonic flight
September 13, 1970: First landing at Heathrow
September 26, 1973: First non-stop flight across the Atlantic
November 23, 1973: Prince Philip flies Concorde for the first
time
January 21, 1976: First commercial flight
November 22, 1977: BA and Air France start services to New
York
July 13, 1985: Phil Collins uses Concorde so he can sing at the
US
and UK Live Aid charity concerts on the same day
July 25, 2000: Air France Concorde crashes near Paris, killing
113
people
August 15, 2000: BA takes Concorde out of service
November 7, 2001: Passenger services resume after safety
improvements
April 10, 2003: Concorde retirement announced by BA and Air
France
May 31, 2003: Last Air France Concorde flight
17. October 24, 2003: Last BA Concorde flight
To mark the anniversary, below is a gallery of Concorde’s best
pics.
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Concorde's final flight: A decade after the aircraft last went
supersonic we look back at its illustrious h...
Go to this issue's
21. Table of Contents.
J A N U A R Y 1 9 7 7
(The online version of this article appears in two parts. Click
here to
go to part one.)
But, in late summer, Britain's negotiations in Brussels, led
by Edward Heath, became sticky: the French were
beginning to raise the objections that were to sink Britain's
application. Then, from Brussels, came requests for
positive movement on the supersonic project. But the two
airframe companies, BAC and Sud had not yet decided
what sort of plane they were building. In September they
were directed to produce an agreed-upon version; the two
chief designers spent one day doing just that. In October
the briefest of outline specifications, contained in fourteen
pages, was delivered to the Ministry of Aviation. For
Amery, it was enough.
As Treasury opposition became more forthright, Amery's
footwork became niftier. First he said that France was
22. insisting on concluding the agreement -- otherwise she
would proceed on her own. (In fact it is extremely doubtful
whether France had the capability to do so; and where the
pressure was coming from is equally unclear, as France did
not even have a government at the time.)
Then, early in November, Amery presented the draft of the
agreement he was proposing to sign. Both the British
Treasury and the French Finance Ministry were appalled to
discover in the agreement that if one country should pull
out of the project unilaterally, it would have to bear all
development costs incurred by both countries.
Amery received delegations from both ministries asking
that the offending clauses be removed. He told the French
not to worry unduly: the treaty was so worded only
because British resolve in such matters had been known to
waver. The next day he told the British Treasury that the
clauses were necessary because the French were not
trustworthy, and that the French had already agreed to
23. them anyway.
On November 29, in London, Amery, together with the
French ambassador to Britain, signed the treaty. "This
aircraft," Amery told the House of Commons that
afternoon, "has every chance of securing a substantial part
The Story of the Concorde - 77.01 (Part Two)
of the world market for supersonic airliners. This is a
chance that will not return."
THE first setback to all the hopes vested in the
supersonic project came six weeks later. On January 14,
1963, General de Gaulle told a packed press conference at
the Elysee Palace in Paris that Britain was not yet ready to
enter the Common Market. But, the General added
pointedly, nothing would prevent continued cooperation
between Britain and France -- "as the two countries have
proved by deciding to build together the supersonic
aircraft, Concorde." The project, he said would be a
guarantee of Britain's sincerity in any later application she
might wish to make. In brilliant stroke the General denied
Britain the Concorde project's political goal -- and ensured
that Concorde nonetheless would go ahead.
The subsequent history of Concorde is riddled with similar
disappointments. The deficiencies in the joint design
produced, under political pressure, by BAC and Sud
became quickly apparent. In 1963 it was discovered that
24. the plane would fall short of New York by 500 miles; the
first major design took place, and so did the first official
reappraisal of costs, raised to £275 million, compared with
the maximum estimateof £95 million. The STAC report
had made. There was a further redesign in 1965: by 1966,
the costs were given as £45 million ($1.26 billion).
As work progressed, the very fine margins of original
concept -- which Dietrich Kuchemann judged "just
possible" -- became increasingly clear. The payload
allowed for represented only 6 percent of the plane's
overall weight -- compared with 12 percent for a Boeing
707 or a VC-10 -- and each time design snags increased
the weight of other equipment, that percentage was further
reduced. The original payload spoken of had been 150
passengers but this was soon reduced to 130; by 1968 it
was found that this was no longer attainable and the
fuselage, wings, and undercarriage had once more to be
designed. In 1969, the cost £730 million ($1.75 billion); it
rose to £1096 ($2.63 billion) by 1975. No one now
mentions 150 even 130 passengers. British Airways hoped
to fly into New York with 100. To Washington, because of
the extra 200 miles, they cannot take more than eighty, and
with Atlantic head winds some flights this winter have had
a limit of seventy out of Bahrain, because of the heat, they
can take off with only seventy-one.
The Story of the Concorde - 77.01 (Part Two)
As the overall weight of the plane kept increasing so did
the job required of the engines. The original specification
was for thrust of around 30,000 lbs; the Olympus engines
25. now powering Concorde provide 38,000 lbs, and the cost
of developing them soared. As thrust increased, so did
engine noise -- while world environmental standards grew
stricter. In 1975 the British government dealt with this
problem by exempting Concorde from its noise
requirements at Heathrow. The first studies made by the
Greater London Council showed that Concorde violated
those requirements on 75 percent of its takeoffs, although
the British Aircraft Corporation forecast that this
proportion would be reduced as pilots became more expert
at noise-abatement procedures. The Greater London
Council's figures also cast light on another of the plane's
characteristics: its noise "footprint," whereby far more
people are affected by the noise from Concorde than from
other planes. Concorde disturbed twice as many people on
takeoff as a 707, the GLC judged, and ten times as many
as a Lockheed TriStar.
Air France's first takeoff from Dulles, on May 24, 1976
26. registered 129 PNdB; the British Airways pilot who
followed sought to minimize the effect by taking a
different runway, thus avoiding the noise-measuring
apparatus; Transportation Secretary Coleman summoned
the British ambassador the following day and left him in
no doubt what he thought of this maneuver. In the first
months of taking off from Dulles, Concorde's noise
readings reached 130 PNdB, with an average of 120. The
average for a 707 over the period was 113.
The 707 is the plane with which British officials are
happiest to see Concorde compared; Concorde, they argue,
is in the same ball park. But as they well know, the major
airlines will be replacing their 707 fleets at the end of the
decade; their successors will be appreciably quieter.
Concorde already suffers drastically in comparison with
the 727 while it was recording the 120 average at Dulles,
that for a 727 was 104.
The other major environmental argument considered at the
27. Washington hearings concerned Concorde's effects on the
stratosphere and in particular on the ozone layer. Coleman
declared that he could not "ignore the possibility that the
six flights proposed by the British and French may result
in some increase in the rate of nonmelanomic cancer."
British Minister Kaufman had argued that it would be
unreasonable to ban Concorde given that "military aircraft
The Story of the Concorde - 77.01 (Part Two)
have for long flown supersonically and at great altitude
over the United States." Coleman agreed that he could not
ban Concorde while the United States permitted other
possible pollutants such as aerosols and refrigerants. At
almost the same time the World Meteorological
Organization, a UN agency in Geneva said that thirty to
fifty supersonic transports would not have a significant
effect on the ozone layer, and that "present supersonic
flights by military air craft and rockets" were too few to
cause concern. But, the WMO added, a "large fleet" -- 200
to 300 -- of supersonic planes could have a noticeable
effect.
But, say the environmentalists, any go-ahead for the
Concorde gives it an advantage of the sort- that the SST's
backers never won. And if Concorde is allowed to fly,
what chance will the environmentalists have of defeating
28. the newer and far greater threat of the B-1 bomber, the
USAF's planned supersonic successor to the B-52, on
whose behalf the military-industrial lobby is now
campaigning? The USAF wants a fleet of 244 B-1s -- the
cost is at present estimated as $21.4 billion -- by 1985. Its
advocates will use Concorde to demonstrate that
supersonic flight is here to stay; all the more important, the
environmentalists counter, to stop Concorde now.
THUS Concorde's noise problem, despite Morien
Morgan's early, devout hopes, was never solved. Another
set of early predictions for Concorde which have remained
unfulfilled are those concerning the plane's market
prospects. STAC had spoken of a world market for
supersonic airliners of 150 to 500 by 1970; in 1962 the
British government had considered 100 sales of Concorde
as not especially optimistic. (They argued then that its
operating costs would be "comparable" with subsonic
planes.) Through the 1960s the manufacturers made much
of the "options" which had been placed for the plane: the
highest figure achieved was seventy-four, by sixteen
airlines, in 1967. In the same year BACs sales manager
was predicting, "on the most pessimistic assumptions,"
sales of 225 Concordes by 1975.
But there was a vital difference between the options held
by BAC and those which a major manufacturer normally
obtains. When Boeing began the 747, it asked the world's
airlines what sort of plane they would like to operate;
when it decided to go ahead and build, it did so with firm
promises to buy, providing the plane met their
The Story of the Concorde - 77.01 (Part Two)
29. specifications, from Pan Am, TWA, Lufthansa, and BOAC
(now British Airways).
This was not the case with Concorde. BAC's commercial
manager recently wrote: "It must be the only airplane ever
launched without some preliminary understanding with the
airlines of what their requirements were and what the
market for it might be." Charles Tillinghast, then resident
of TWA, was with a British journalist on the day the
Anglo-French agreement was signed. In some
embarrassment he showed her the newspaper report and
said, "No one asked us if we wanted the plane." When
TWA, like Pan Am, withdrew its "options" in 1973, it cost
them no financial penalty to do so.
The only two airlines to buy the planes remain the two
respective national carriers, British Airways and Air
France. British Airways was virtually ordered to do so by
the British government; the price was a very favorable £23
million each, against the present selling price of £35
million ($56 million), and they extracted a guarantee from
the government to underwrite their losses. In 1974 British
Airways calculated that these losses could be as much as
£25 million a year.
The most determined attempt Britain ever made to escape
from its commitment came in 1964, when a Labour
election victory ended the thirteen-year Conservative
regime. The new aviation minister, Roy Jenkins, was
dispatched to Paris to negotiate a withdrawal, but the
French merely pointed to the terms of the agreement. The
British attorney general said that Britain might have to pay
up to £200 million ($560 million) in damages, and the
government backed down. At several subsequent points
both the British and the French governments wanted to end
the project, but in view of the wording of the treaty, neither
30. side could afford to let it appear that it was the one seeking
cancellation, for the other would see a chance of recouping
its own expenditure and would maintain that it, of course,
wanted to carry on.
When Labour's rule ended in 1970, Edward Heath asked
his government's "think tank" -- a body of unaffiliated
intellectuals, headed by Lord Rothschild, and known
formally as the Central Policy Review Staff -- to deliver a
judgment on Concorde. When it came, it was simple
enough. "Concorde," it began, "is a commercial disaster."
But the report did accept that the plane carried
considerable importance in terms of diplomacy and foreign
The Story of the Concorde - 77.01 (Part Two)
relations. It could not recommend cancellation: that was a
decision for government.
By now the wheel had turned full circle, for Heath had
decided again to seek entry to the Common Market. The
minister responsible for Concorde at the Department of
Trade and Industry -- which had earlier subsumed the
Ministry of Aviation -- was John Davies. "If Concorde had
been merely a business decision," he says now, "there was
no possible reason for carrying on." But, he adds,
"Pompidou undoubtedly regarded Concorde as a
touchstone of Anglo-French relations. If we had pulled out
he would have regarded it as the biggest stab in the back."
THE first British Airways Concorde entered service in
January 1976 with an inaugural flight to the tiny Persian
Gulf state of Bahrain; on the same day, Air France flew to
Rio. The British press, which with a few honorable
31. exceptions has maintained an uncritical and jingoistic
attitude toward the plane, was ecstatic. "Triumphant Debut
by Concord -- Concorde-Champagne and Caviar at Magic
Mach 2" were the headlines in Conservative Daily
Telegraph. Its air correspondent, Air Commodore E. M.
Donaldson, wrote: "This without doubt must be the
greatest leap forward in air travel the world has ever
known."
Herb Coleman, the London editor of Aviation Week, also
on that first flight, was less sanguine. Concorde gives an
"adequate" ride, he says. "The seats are very comfortable,
up to first class forward. But it's less adequate if you want
to around. If you're used to wide-bodied planes Concorde's
cabin tends to close around you -- it's like being back in
Constellation days. There's a high noise level although not
enough to inhibit conversation. Apart from that it's just
another aircraft as far as I'm concerned."
Since then Concorde has been flying to Bahrain with forty
passengers or so; one flight had only twenty-one. Air
France has been flying to Rio with 80 percent loads.
British Airways flights into Washington have been over 90
percent full -- although ten with at least twenty, sometimes
as many as thirty-two, of the 100 seats "roped off" because
the plane is operating at the limits of its range. Expenditure
continues: $1.35 million for new passenger facilities at
Heathrow: $900,000 for an advertising campaign in
Britain, with commercials showing a silent Concorde
flying through broken cloud, and the exhortation, "Fly the
future -- fly the flag."
The Story of the Concorde - 77.01 (Part Two)
32. Geoffrey Rippon and Julian Amery remained quite
unabashed at their part in lumbering with so enormous a
debt, even though it is now accepted that much of Britain's
present ills result from excessive public expenditure. From
them, and from Sir Morien Morgan, have come the most
optimistic scenario for the future of Concorde," from the
British Aircraft Corporation itself, which is still using its
supporters among the British correspondents to promulgate
its euphoric views.
The scenario runs as follows. Concorde will be allowed to
land at Kennedy and will win flying rights for its route to
Australia (for much of 1976, tightly snagged in India). It
will become so popular that Pan Am and TWA will be
compelled to operate Concordes too. Later Britain, France,
and the United States will together develop the next
generation of supersonic airliners. (BAC has already let it
be known that it is considering plans already for a
Concorde successor with McDonnell Douglas.) Concorde
will have ensured Britain's survival as a major aviation
power.
The most remarkable aspect of the Amery/BAC vision is
that it fails to profit in any way from the experience of
Concorde. There is the astronomical and the terrifying cost
escalation, of such a project. Before the last Conservative
aerospace minister Michael Heseltine, left office in 1974,
he asked his Ministry for an estimate of how much it
would take to develop a second-generation Concorde. The
answer was $7.2 billion. In 1976 Rolls-Royce produced a
new estimate: $11 billion.
There is also the failure to draw any lessons out the course
of aircraft development. The clear moments of progress in
the history of civil aviation were those where new models
of aircraft decisively widened the world air travel market.
33. Concorde's first advocates such as Morien Morgan,
claimed that this was because most of these models could
fly faster than their predecessors: Concorde was thus a
logical forward.
But speed was not the decisive or sole factor as the models
replaced the old ones. Expansion of the world market took
place because the new planes were supposed to reduce
passenger costs. Concorde was to be the first major
development which could not create a new market, but
would seek to take a slice of markets that already existed.
It would not reduce costs, but increase them, by up to three
times per passenger mile: a ratio disastrously magnified by
the actions of OPEC in 1973 and 1974.
The Story of the Concorde - 77.01 (Part Two)
It is true, as TWA's president, Ed Meyer, conceded last
summer, that there is a market for supersonic passenger
flight. "There is going to be a certain group of first-class
passengers who are prepared to pay for speed, and in no
way can we compete," he said. And pay they must. After
hard bargaining within the International Air Transport
Association (IATA), British Airways agreed that New
York-London Concorde fare should be the present first-
class fare plus 20 percent. They quote $756 for the single
New York-London fare, against a subsonic first-class fare
of $625, economy of $292. (Of course there are cheaper
subsonic available too: return fares of $541 for a minimum
21-day stay, $325 for booking two months ahead.) Ed
Meyer estimated that if Concorde should land at Kennedy,
TWA would lose revenue of around $20 million a year,
against TWA's total turnover of $1.3 billion. But it made
no economic sense for TWA to buy a Concorde, he said,
34. nor even to lease space in a British Airways plane.
It is also true that the major U.S. manufacturers maintain
small departments to keep abreast of supersonic
developments. But the main thrust is in quite another
direction: toward planes that will be quieter and will
consume less fuel, thus meeting today's twin demands of
economy and ecology. The three main U.S. companies
appear to agree that the 200-seat plane for short and
medium ranges is the next logical step. McDonnell
Douglas is talking of a DC-X-200, effectively a scaled-
down DC-10; Boeing has designated its next model the
7X7, a medium-sized wide-body plane, but is far from
hard on its specifications. The first problem for the
manufacturers, already hit by the recession in aviation that
followed OPEC, is to raise development finance. Indeed,
this difficulty may force airlines to buy planes that are
essentially derivatives of models flying today -- and last
summer British Airways decided to replace some of its
707s with a long-range version of the Lockheed TriStar,
requiring only minimal modification. Boeing, meanwhile,
estimates that an entirely new 7X7 would cost around one
billion dollars -- against which the projected figures for a
new supersonic airliner recede into absurdity.
CONCORDE certainly won the British and French
aircraft industries a good share of publicity. Whether it has
helped keep them healthy, as STAC proposed, is a
different matter.
The Story of the Concorde - 77.01 (Part Two)
The likely but bleak alternative to the Amery scenario is
that no more than the sixteen Concordes at present
36. future. It has cost at least fifteen times the original
estimates. It is described as a "commercial disaster" by a
review committee of one of the countries that built it. It is
besieged by the environmentalists. The Concorde is the
benighted offspring of Anglo-French diplomacy and
once-and-future dreams of glory in the skies. Now its
builders are trying to keep it from crashing in a sea of
red ink
by Peter Gillman
(The online version of this article appears in two parts. Click
here to
go to part two.)
THE supersonic Concorde has suffered a bewildering
year. Last February U.S. Transportation Secretary William
Coleman decided to allow the supersonic plane into Dulles
and Kennedy airports for a sixteen-month trial period. But
then the New York Port Authority banned Concorde for
six months so that it could monitor the results of
Concorde's noise tests as it flew in and out of Washington.
37. British Airways and Air France, the only two airlines so
far to have bought the plane, at first appealed the ban, then
decided to postpone their suit until New York announced
its decision -- expected momentarily. Jimmy Carter won
big headlines in Britain for his opposition to the plane
during his presidential campaign: afterwards he "clarified"
his position by saying a final verdict would depend on the
noise and pollution tests. British Airways and Air France
had hoped to be flying Concorde into Kennedy by
Christmas: recently they have been saying that if New
York approves the plane, they will begin operations by the
spring.
No other plane has had to undergo such preliminary
tribulations. It was an unusual experience for British
politicians and officials to participate in the rough-and-
tumble of American political lobbying, or take part in a
rowdy debate with Concorde opponents, as they did when
Supersonic Bust: The Story of the Concorde - 77.01
38. they came to Washington for Mr. Coleman's hearings last
January. The British pitched their arguments before
Coleman at a modest level. Gerald Kaufman, Harold
Wilson's former press aide, now Britain's minister of state
for industry explained that they merely sought four
journeys a day to New York and two Washington. All that
they wanted was for Concorde to be given "a chance."
What Kaufman and his officials meant was the chance to
save face. Already Britain, and France spent £.46 billion
($2.3 billion) to reach this (and a London political
economist has recently argued that the true cost is roughly
three times this amount).
1
As Kaufman knew, it is
imposible for the two countries to recover any but a tiny
part of this staggering total. It may be true that Concorde's
progenitors spoke of a payload of 150 passengers, while
Concorde has been flying to Washington this winter with a
limit of seventy; it may be true that they spoke of operating
costs "comparable with" other planes, while it costs three
times as much per mile to carry a passenger in Concorde as
in its subsonic rivals. But let us fly into New York, the
British pleaded, and we can pretend that Concorde is not
the most disastrous investment decision Britain has made
since the war.
CONCORDE is already, in effect, twenty years old. The
decision to begin the supersonic project was made in 1956,
the year of Suez, Britain's last great imperialist gesture. It
was a time when Britain was still enjoying postwar
39. expansion, and had not yet had to face the economic
consequences of the loss of empire. It was a time of the
technological imperative, when the first suggestions that
technology did not of itself represent progress were only
just being made. And it was a time when Britain still
believed that she had the capacity and expertise to rank
with the world's major industrial powers.
For British aviation, the most traumatic event after the war
was the disaster of the Comet. Early in 1954 two Comets
exploded over the Mediterranean, killing all on board. The
Comet was grounded for two years, and by the time it was
ready to fly again, the 707 and the DC-8 had built up an
unassailable lead.
It fell to the Royal Aircraft Establishment at Farnborough,
a country town thirty miles southwest of London, to carry
out the painful examination of the Comet crashes.
Farnborough concluded that the explosions had been
Supersonic Bust: The Story of the Concorde - 77.01
caused by metal fatigue at the Comets' windows. Faults in
the manufacturers' preproduction tests had led them to
underestimate the effects of pressurization.
It was from the experts at Farnborough, committed to
technological advance, that the pressures for a supersonic
project now came. One of the most important characters in
the story of Concorde is Morien Morgan, a short, ebullient
Welshman, who now, as Sir Morien, is master of Downing
College, Cambridge. In 1956 Morgan was Farnborough's
deputy director, and ideally placed to give the project its
initial momentum. Later he moved into senior posts at the
40. Ministry of Aviation headquarters in London, enabling
him to keep the project on course. His enthusiasm and his
advocacy were to prove vital.
One reason that Concorde is flying today becomes clear
when one talks to Sir Morien. It stems from the
competitiveness and envy toward the United States that
grew out of decisions made in the heat of World War II.
When America entered the war the British agreed to
concentrate on building fighters and bombers, leaving
transport planes to the United States; in 1945 the United
States was much better placed to move back into civilian
transport planes. "That was a bit heartbreaking," says Sir
Morien. But Concorde, he adds, enabled Britain "to look
the Americans firmly in the eye again."
In fact, the main reason Britain left transport planes to the
United States was that the United States was well ahead in
the field anyway. In 1941 the civilian Douglas DC-3 and
DC-4 were already flying and the Lockheed Constellation
was well under way. Britain's attempts to get back into the
civilian market were painful; even before the Comet, flop
followed flop.
In October 1956, largely at Farnborough's prompting, a
meeting was held at the Aviation Ministry headquarters in
London, attended by the heads of Britain's nine airframe
and four engine companies, and by officials from
Farnborough, including Morien Morgan. The Ministry's
permanent secretary, Sir Cyril Musgrave, chaired the
meeting, and as he recalls, the choice presented to it was
stark. "All the major airlines were buying the 707 or the
DC-8 and there was no point in developing another
subsonic plane. We felt we had to go above the speed of
sound, or leave it."
41. The manufacturers at the meeting were dubious: their
initial attitude, says Sir Cyril, was, "It's a bright idea as
Supersonic Bust: The Story of the Concorde - 77.01
long as the government pays for it." The British
government had indeed demonstrated that it was prepared
to underwrite the mistakes of the British aviation industry,
having paid out over $140 million by then for its various
flops. The Treasury was now showing increasing
opposition to financing aviation schemes, but that, for
Morgan and other supersonic supporters, would all be part
of the struggle.
ON November 5, 1956, at Farnborough, the first meeting
of the Supersonic Transport Aircraft Committee, known as
STAC, was held. On it were representatives of
government, business, the airlines, and Farnborough; its
chairman was Morien Morgan. The committee's goal, if
not its formal brief, was to produce a report demonstrating
that a supersonic passenger plane was both feasible and
desirable.
It succeeded in its first objective with a large slice of good
luck. Farnborough had already made a preliminary
examination of the problems of designing a supersonic
airliner. As Morgan later commented, "Only silly
aeroplanes emerged." The one plane that would fly
nonstop from London to New York -- to STAC, the prime
route -- would carry fifteen passengers and cost five times
as much to operate as existing subsonics. When STAC
began its work, it had no clear idea of how it was going to
build the plane. But working at Farnborough at that time
was one of the brilliant German aerodynamicists for whose
42. services Britain and the United States had competed in
1945: Dietrich Kuchemann. It was Kuchemann's work
which made Concorde possible. In 1957 he declared that a
supersonic passenger plane with a thin delta wing was
"just possible."
Early in 1959, after a battery of tests had been completed,
the STAC report was ready. Not surprisingly, it
recommended that the supersonic project proceed. It was
forwarded to the Ministry's controller of aircraft with a
letter, written by Morien Morgan, of extraordinary
enthusiasm and urgency, and with none of the hesitations
of Kuchemann's basic aerodynamic verdict, none of the
social implications of building a supersonic plane for an
elite dozen or so passengers expressed.
Morgan wrote: "We feel it right to proceed with the two
supersonic aircraft outlined above, and we must emphasize
that a decision not to start detailed work fairly soon on the
transatlantic aircraft would be in effect to opt altogether
Supersonic Bust: The Story of the Concorde - 77.01
out of long-range supersonic transport field. Since we
would never regain a competitive position this could have
a profound effect on the pattern of our Aircraft Industry
and on our position as a leading aeronautical power."
Seventeen years after it was produced, and even though the
plane it recommended has now been built, the STAC,
report remains officially secret. There is no Freedom of
Information Act in Britain; secrecy and anonymity remain
fundamental to the way government decisions are reached.
Had the issues involved been discussed and examined in
43. public, it is doubtful whether Britain and France would
ever have built Concorde. But the very first time the
British Parliament was permitted to debate the project was
in December 1962 -- one month after an Anglo-French
treaty had committed Britain irrevocably to the plane. In
the United States, public debate on the Boeing led to its
cancellation in 1971.
But why should the British government withhold the
STAC report even now? The answer can only be that there
is considerable embarrassment at the report's estimates of
the costs of the supersonic plane, and of its commercial
possibilities.
STAC did say that costs were "difficult to estimate at this
stage," but promptly overrode that caveat by stating that
they would be in the range of £59 million to £95 million
($165 million to million), depending on range, speed, and
payload (At that time two versions were being considered:
a Mach 1.2 plane carrying 100 people for 1500 miles, and
a Mach 1.8 plane carrying 150 passengers from London to
New York.) Even if the figure of £95 million ($266
million) is taken, and Professor Henderson's more
pessimistic formulation is ignored, STAC was off by a
factor of around 15. The British government's latest figures
of development costs, shared between Britain and France
are £l154 million. To that must be added production costs
and losses sustained through operating Concorde by
British Airways and Air France bringing the total to
around £1460 million.
STAC's optimism over costs was matched only by its
optimism over the plane's market prospects. It concluded
that by 1970 there would be a world market for 150 to 500
supersonic planes. Conjoining the two equations, Morgan
estimated that a supersonic plane could recover its entire
44. research and development costs on just thirty sales.
Supersonic Bust: The Story of the Concorde - 77.01
There is nothing exceptional in cost estimates being
wrong; one American study has shown estimates for
military projects have been too low by an average factor of
6.5. But in the case of Concorde more than mere
miscalculation is involved. Dietrich Kuchemann died in
March 1976. Shortly before, he described how the head of
Farnborough's aerodynamic department, Philip Hufton, sat
down and invented the figures. "It was done on the basis of
let me see, what will the politicians stand," Kuchemann
said. He added: "In the whole STAC report, those
estimates are the only thing that are rubbish. I have a very
bad conscience about that."
WITH the presentation of the STAC report, a powerful
mix of brilliant aerodynamics and disreputable
propaganda, the political battle over Concorde was joined.
The British Conservative party had been in power since
45. 1951. Churchill had been prime minister then, followed, in
1955, by Anthony Eden; Eden had departed after Suez. His
successor, Harold Macmillan, was represented as part of
the "meritocratic" strain of modern conservatism, but his
Cabinet still contained such members of the old guard as
Lords Salisbury and Kilmuir. And the story of Concorde
was to demonstrate that the age of irrational decision-
making was not yet past.
The first minister of aviation to take up Concorde was
Aubrey Jones, a young economist who at once foresaw the
inevitable Treasury opposition to the project. He proposed
to his officials that he seek a European partner for the
venture as a way of sharing the costs and pre-empting
Treasury objections. Jones was also one of the group of
Conservatives who had been disappointed when Britain
had not joined the European Common Market, formed in
1957. To him and others like him, a joint venture on so
major a project offered some kind of "surrogate" for entry.
46. Jones made the first tentative proposals when he met the
French transport minister at the Paris air show in the
summer of 1959, and also asked two British firms to carry
out preliminary studies on the designs suggested by STAC.
In October 1959, the Conservatives won their third
successive general election and Jones was replaced at the
Ministry of Aviation by Duncan Sandys, a member of
Churchill's wartime Cabinet who had organized Britain's
defenses against Hitler's flying bombs and rockets. Sandys
was now charged with organizing the British aircraft
industry into more compact and -- it was hoped -- more
Supersonic Bust: The Story of the Concorde - 77.01
efficient groups. Britain's thirteen aircraft firms dwindled
to four; on the airframe side, the British Aircraft
Corporation and Hawker-Siddeley on the engine side,
Bristol-Siddeley and Rolls-Royce.
Sandys made a tour of European capitals -- Rome, Bonn,
47. Paris - in search of a partner for the supersonic project.
The strongest interest came from France. Sandys now
presented the scheme to the Cabinet, adopting the
arguments Morien Morgan had used to persuade the
Ministry itself in 1956. If Britain was to continue as a
power in world aviation, Sandys told the Cabinet, it had to
build a supersonic. "We have to go on," Sandys said, "or
opt out."
Sandys left the Ministry, having completed reorganization,
in July 1960, to be succeeded by Peter Thorneycroft, a
former chancellor of the exchequer. But continuity was
ensured by the presence at the Ministry of Geoffrey
Rippon, a young Conservative MP who served as the
minister's parliamentary secretary. Rippon's role was
crucial. He was another pro-European, deeply committed
to the supersonic project, who formed an alliance with
Morien Morgan and a handful of other senior officials to
see the project through. As chairman of a small steering
48. committee at the Ministry, Rippon accepted that it had two
tasks. The first was to keep the project from Treasury
scrutiny for as long as possible; the, second was to ensure
French cooperation.
Rippon had total disdain for the Treasury. "They have no
concept of the national interest" he declared. "They judge
everything with the narrowest possible perception." To
prevent the Treasury from learning of the project's
progress, he decreed that as little as possible should be
committed to paper. "We were small, informal, united," he
said later, "a band of brothers."
But Rippon's most decisive single action concerned the
STAC report. When completed, it bore the melodramatic
imprint, "Confidential: UK Eyes Only." Though it remains
secret in the UK today, Rippon gave a copy of the report to
the French.
The STAC report was handed over, on Rippon's authority,
in the summer of 1960. Containing the aerodynamic secret
49. of Concorde, it convinced the French that the project was
feasible; and if the French were to come in on the deal,
they had to learn the secret at some time. But the delivery
of the report two years before the deal was formally agreed
Supersonic Bust: The Story of the Concorde - 77.01
upon provided the project's supporters in Britain with the
argument that if Britain decided not to build the plane,
France would go ahead anyway.
Peter Thorneycroft -- even while his subordinate Rippon
was vigorously pursuing the French -- did make one effort
to cushion Britain from the financial implications of the
project, which he was certain would far exceed the STAC
estimates. Better than a partnership with France,
Thorneycroft judged would be one with the United States.
Britain would clearly have only junior status, but the
financial burden would be eased, and there would be an
assured market among the American airlines.
In 1961, Thorneycroft discussed collaboration with
American officials in Washington; both they and Boeing
visited the Ministry of Aviation in London. Eventually the
Americans turned the idea down, and one of their
negotiators later told a British official that they doubted
whether the British plan for a Mach 2 aircraft in
conventional metal was technically feasible, and whether
the proposed payload, in the 125-150 range, would be
economic. As it turned out. the American solution proved
50. even more dubious: Boeing aimed to build a titanium
passenger plane carrying 250 people at almost Mach 3, but
the company's inability to design an economic version led
eventually to cancellation of the SST in 1971. In 1961,
however, their decision to turn down the British proposals,
and to continue with their own research, helped create a
sense of urgency which Concorde's protagonists skillfully
turned to their own advantage. Thorneycroft himself now
looked again to France.
BRITISH manufacturers, meanwhile, had been
continuing technical discussions with British government
officials, and with manufacturers in France. These
discussions were through with confusions whose
resolution was to prove most costly.
First there was the airframe. In 1960 the British
government had given the new British Aircraft
Corporation a $1 million contract for a feasibility study.
BAC was also asked to have informal talks with the
Toulouse firm Sud-Aviation, which was drawing up its
own preliminary plans. Sir Archibald Russell, BAC's chief
supersonic designer, visited his old friend Pierre Satre,
Sud's technical director. Russell's first approach was
cautious. Considerable savings could be achieved, he
argued if each company built separate aircraft but shared
Supersonic Bust: The Story of the Concorde - 77.01
the components, such as the engine, and the hydraulic and
electrical systems. But this was not enough for the
politicians: the Ministry of Aviation told the companies to
amalgamate their work completely.
51. The problem was that the two companies favored entirely
different versions. BAC was pursuing the Mach 2
transatlantic plane that had been the rationale behind
STAC; Sud preferred a medium-range plane (which STAC
had also considered). No politician at that time was read
make a decision.
A bitter commercial battle was also being fought over the
choice of engine. The contenders were the two new British
engine firms, Bristol-Siddeley and Rolls-Royce. Rolls-
Royce showed considerable realism toward the problem of
noise. In a two-and-a-half-inch-thick report on the engine
requirements, Rolls pointed out that the New York Port
Authority had already introduced a takeoff level of 112
Perceived Noise Decibels (PNdB) today's limit at
Kennedy, and that Heathrow was considering stricter
limits. Rolls concluded: "The next generation of subsonics
is being designed to be appreciably quieter -- of the order
of 100 PNdB -- and this is the order to which the
supersonic should be designed throughout."
Rolls's honesty did not win them the contract, and they
were politically outflanked by Bristol-Siddeley. whose
managing director, Sir Arnold Hall, had realized at an
early stage that the only way the project would go ahead
was as a joint production. He paid a discreet visit to the
French aero-engine company SNECMA and suggested a
deal; when the governments came to consider who should
build the engine, Bristol Lind SNECMA were able to point
to the progress toward collaboration they had already
made. The engine chosen was a "civillanized" version of
the Olympus which Bristol had been developing for the
multirole combat plane the TSR-2 (eventually cancelled by
the Labour government in 1965, after $532 had been
spent).
52. It is clear that the project's supporters had little to
contribute to the noise problem, beyond optimism. Morien
Morgan declared in 1960: "The prize is a golden one. We
will bring tremendous research efforts to bear to the noise
problem." But the Olympus engine was already quite old:
the first version had been used in an RAF Canberra in
1952. And all attempts to reduce noise were entirely
outweighed by the continued increase in power required as
Supersonic Bust: The Story of the Concorde - 77.01
the airframe makers tried to extricate a feasible aircraft
from the confusion over what they were building.
In the political sphere the project was gaining momentum.
In July 1962, Thorneycroft was replaced as the minister
responsible by Julian Amery, the man who finally signed
the Anglo-French treaty. Amery, the fourth of the
ministers to handle the project, was the most passionate in
its favor. He was ambitious. politically adroit, and a
gambler: three characteristics which were to see the project
through. Soon after becoming minister, Amery sent his
new parliamentary secretary at the Ministry. Basil de
Ferranti -- whose family made electronic aviation
equipment -- to Farnborough to assess the project. Ferranti
remembers being impressed by the argument that the plane
would sell "either none at all or a hell of a lot."
The attitude he and Amery took was: "It is a gamble. But if
we can do it with the French, it will halve the ante. So let's
have a go."
By 1962, too, the project had become a vital part of the
Foreign Office's strategy for securing entry to the Common
53. Market, which Harold Macmillan had decided earlier that
year to pursue. A co-production deal was important as an
earnest indication of Britain's European intentions, and the
project demonstrated the kind of industrial expertise
Britain would contribute to the European community.
* * *
ENDNOTE: In May 1976, Professor David Henderson,
newly appointed professor of political economy at
University College, London, argued that the government's
figure of £1.46 billion shared between Britain and France
was a drastic underestimate. It had been reached by adding
the yearly expenditure on the project at the current prices.
if these were adjusted to 1975 prices, and interest charges
of 10 percent added, then the cost of Concorde was not
£1.46 bilion but £4.26 billion ($6.82 billion at the present
exchange rate of $1.60).
Consideration of the "true cost" of Concorde is further
complicated by the pound's fluctuating exchange rate. In
1959, when the first cost estimates were made, the pound
stood at $2.80. Devaluation in 1967 took it to $2.40. In
mid-1973 it was back to almost $2.60 but then its decline
began. in April 1975 it was at $2.40; December 1975,
$2.01; May 1976, $1.82; August, $1.78; September, $1.64;
October, $1.59. In this article, where dollars are used for
Supersonic Bust: The Story of the Concorde - 77.01
British figures they have been converted at the rate
prevailing at that time.