Coefficient

Coefficient (pronounced koh-uh-fish-uhnt)

(1) In mathematics, a number or quantity in an equation placed usually before and multiplying another number or quantity; a constant by which an algebraic term is multiplied; a number, value or item that serves as a measure of some property or characteristic.

(2) In physics, a number that is constant for a given substance, body, or process under certain specified conditions, serving as a measure of one of its properties; a number, value or item that serves as a measure of some property or characteristic.

(3) Acting together (rare except in historic references).

1580s: From the Middle English coefficient (that which unites in action with something else to produce a given effect), from the French coefficient, coined by French mathematician François Viète (1540-1603), from the Late Latin coefficient, stem of coefficiēns, which is a nominalisation of the present active participle of coefficere, the construct being co- (together) + efficere (to effect) from efficio.  The alternative spelling is co-efficient and the adjectival sense “acting in union to the same end” was first used in the 1660s.  Coefficient is a noun & adjective, coefficiency is a noun and coefficiently an adverb; the noun plural is coefficients.

In science and engineering, the word is applied for a variety of technical purposes, including:

(1) In physics, as coefficient of friction, the ratio between (1) the magnitude of the force of friction which a surface produces on an object (moving along the surface or being pressed statically against it) & (2) the magnitude of the normal force which is produced by the surface on the object and which is perpendicular to that surface.

(2) In physics, as drag coefficient, a dimensionless quantity quantifying the amount of hydrodynamic drag force experienced by an object with a given area immersed in a fluid of a given density flowing at a given speed.

(3) In statistical analysis, a coefficient of alienation (or coefficient of non-determination), a numerical measure of the lack of relationship between variables.

(4) In physics, as ballistic coefficient, the ratio of the mass of an object to the product of its maximum cross-sectional area and its drag coefficient, used to measure the object's resistance to deceleration by hydrodynamic drag.

(5) In chemistry, as Bunsen coefficient, the number of millilitres of gas dissolved in a millilitre of liquid at atmospheric pressure and a specified temperature.

(6) In statistics, as Dice coefficient, a statistic used to gauge the similarity of two samples.  It is equal to twice the number of elements common to both sets, divided by the sum of the number of elements in each set.

(7) In naval architecture, as prismatic coefficient, the ratio between the total submerged volume of a vessel's hull, on the one hand, and the product of the length of the submerged portion of the hull with the area of the largest cross-sectional slice of the submerged portion of the hull, on the other.

(8) In naval architecture, as block coefficient, the proportion occupied, by the submerged portion of a vessel's hull, of a rectangular prism with dimensions equal to the maximum beam of the submerged portion of the hull, the length of the submerged portion of the hull, and the draft of the vessel.

(9) In measurement, as temperature coefficient, a number which relates the change of the magnitude of a physical property to a unit change in temperature.

(10) In nuclear engineering, as void coefficient, a number quantifying how the reactivity of a nuclear reactor changes due to the formation of bubbles in the reactor's coolant.

Drag coefficient (CD)

Except in a vacuum, objects in motion are subject to drag, the friction created by air or water interacting with the object’s surface.  This friction absorbs energy the object could otherwise use to maintain or increase speed so, except where drag is required (such as the need for a certain amount of down-force), designers of objects which move, shape them to minimise drag. Historically, the drag coefficient was notated as c_d but it’s also written as c_x & c_w (cd or CD a common form in non-specialist literature).  The CD number is calculated according to a equation, the construct of which varies according to the object to be assessed.  For a car, the equation is:

F = 1/2 * rho * S * Cx * v²

F is the dragging force, in expressed in Newtons (N)

S is the frontal surface of the object in square metres (m²)

Cx is the aerodynamic finesse, which varies depending on the shape of the object

v is the relative speed of the object (the car) compared to the fluid (the air), in meters per second (m/s), separated into vc (object speed) and va (air speed) and written (vc - va)

rho is the density of the fluid, the air, in kilograms per cubic meters (kg/ m³) (approximately to 1.55 kg/m³)

The drag coefficient (CD) is a measure of aerodynamic efficiency, expressed as a number and, as a general principle, the lower the number, the more efficient the shape but the CD is often misunderstood.  It’s not an absolute value which can be used to compare relative efficiency of objects of radically different shapes.  A CD for an aircraft needs to be compared with that of other airframes, not those of a train or truck, the CD calculated by an equation using a variable (the reference area) relevant to the function of the object.  For aircraft, the variable is the wing area because it’s relevant for an object moving in three dimensions whereas for road vehicles, it’s the frontal area, cars and trucks almost always moving forward.  That’s why noting a Boeing 747 has a CD of .031 while a Porsche 911 might return .34 is a meaningless comparison.

1963 Jaguar E-Type S1 (XK-E) FHC (fixed head coupé) (left) and 1962 Volkswagen Type 2 (23 Window Samba).

Even among road transport vehicles, the variability in the equations needs to be understood.  Just because a Volkswagen Type 2 returns a CD of .42 doesn’t mean it’s a more aerodynamic shape than a Jaguar E-Type (XK-E) which produces a notionally worse .44 CD.  The numbers are a product partly of the variable, the frontal area, so the efficiency of the Volkswagen can be assessed only if compared to other, similarly sized vans.

Spat

Spat (pronounced spat)

(1) A petty quarrel; a dispute.

(2) A light blow; a slap or smack (now rare).

(3) A classic footwear accessory for outdoor wear (technically an ankle-length gaiter), covering the instep and ankle, designed to protect these areas from mud & stones etc which might be splattered (almost always in the plural).

(4) In automotive design, a piece of bodywork on a car's fender encapsulating the aperture of the wheel-arch, covering the upper portion of the wheel & tyre (almost always on the rear) and used variously to reduce drag or as a aesthetic choice.  In the US, these tend to be called "fender skirts".

(5) In aviation, on aircraft with fixed undercarriages, a partial enclosure covering the upper portion of the wheel & tyre, designed to reduce drag.

(6) In zoology, a larval oyster or similar bivalve mollusc, applied particularly when one settles to the sea bottom and starts to develop a shell; young oysters collectively, especially seed oysters.

1350-1400: From the Middle English spat (argument, minor scuffle), from the Anglo-Norman spat, of unknown origin but presumed related either to (1) being the simple past tense & past participle of spit or (2) something vaguely imitative of the sound of a dispute in progress.  In use, a spat implies a dispute which is minor and brief.  That doesn’t preclude violence being involved but the word does tend to be applied to matters with few serious consequences but a spat can of course escalate to something severe at which point it ceases to be a spat and becomes a brawl, a fight, a murder, a massacre or whatever the circumstances suggest is appropriate.  Otherwise, a spat is synonymous with words like bickering, brouhaha, disagreement, discord, falling-out, feud, squabble, tiff or argument.

As a descriptor of the short gaiter covering the ankle (which except in technical and commercial use is used only in the plural), use dates from 1779 as an invention of American English and a shortening of the trade-terms spatterdash (or splatterguard) (long gaiter to keep trousers or stockings from being spattered with mud), the construct being spatter + dash (or guard), the former the same idea as the noun dashboard which was a timber construction attached to the front of horse-drawn carriages to protect the passengers from mud or stones thrown up when the beasts were at a dash.  In cars, the use of the term dashboard persisted although the device both shifted rearward (aligned with the cowl (scuttle) & windscreen) and changed in function.  In aircraft where the link to horse-drawn transport didn’t exist, the preferred equivalent term became “instrument panel”.

Stanley Melbourne Bruce (front row, second from left) in spats, official photograph of his first cabinet, Melbourne, 1923.

Spats date from a time when walking in cities could be a messy business, paved surfaces far from universal.  As asphalt and concrete became commonplace in the twentieth century, spats fell from frequent use though there were those who clung to them as a fashion accessory.  Stanley Melbourne Bruce (1883–1967; prime minister of Australia 1923-1929) liked spats and wore them as late as the 1940s but historians of fashion note it's said nothing was more influential in their demise than George V (1865–1936; King of the United Kingdom 1910-1936) eschewing them after 1926.

However, despite losing the imprimatur of the House of Windsor (ex Saxe-Coburg and Gotha), when Disney in 1947 created Scrooge McDuck (the world's richest duck, noted for diving into his vast "money bin" to swim among the cash), spats must still have been associated with wealth and uncle Scrooge has almost always been depicted sporting a pair.

Spats (left) and gaiters (centre & right).  Historically, gaiters were either medium (mid-calf) or long (reaching to the knee) while the shorter variations, extending from ankle to instep, were known as spats.  In the fashion industry, the terms gaiters and spats are often used interchangeably and except among the equestrian and other horse-oriented crowds, they now exist only as a fashion item, improvements in the built-environment meaning the need for them as functional devices has diminished.  They days, spats tend to be seen only in places like the Royal Enclosure at Ascot or smart weddings (used as a wealth or class signifier) although variations are still part of some ceremonial full-dress military uniforms.  Technically, a spat probably can be called a “short” or “ankle-length” gaiter but it’s wise to use “spat” because gaiters are understood as extending higher towards the knee.

Lindsay Lohan in SCRAM bracelet (left), the SCRAM (centre) and Chanel's response from their Spring 2007 collection (right).

Spats for the twenty-first century: Before Lindsay Lohan began her “descent into respectability” (a quote from the equally admirable Mandy Rice-Davies (1944-2004) of MRDA fame), Lindsay Lohan inadvertently became of the internet’s early influencers when she for a time wore a court-ordered ankle monitor (often called “bracelets” which etymologically is dubious but rarely has English been noted for its purity).  At the time, many subject to such orders often concealed them under clothing but Ms Lohan made her SCRAM (Secure Continuous Remote Alcohol Monitor) a fashion statement, something that compelled the paparazzi to adjust their focal length to ensure her ankle of interest appeared in shots.  The industry responded with its usual alacrity and “ankle monitor” purses were soon being strutted down the catwalks.

Chanel's boot-mounted ankle purse in matching quilted black leather.

In one of several examples of this instance of Lohanic influence on design, in their Spring 2007 collection, Chanel included a range of ankle bags.  Functional to the extent of affording the wearing a hands-free experience and storage for perhaps a lipstick, gloss and credit card (and the modern young spinster should seldom need more), the range was said quickly to "sell-out" although the concept hasn't been seen in subsequent collections so analysts of such things should make of that what they will.  Chanel offered the same idea in a boot, a design actually borrowed from the military although they tended to be more commodious and, being often used by aircrew, easily accessible while in a seated position, the sealable flap on the outer calf, close to the knee.

On the Jaguar 2.4 & 3.4 (1955-1959, top row; later retrospectively named Mark 1), full-sized spats were standard equipment when the standard wheels were fitted but some owners used the cut-down versions (available in at least two designs) fitted when the optional wire wheels were chosen.  For use in competition, almost all drivers removed the spats.  The Mark 2 (bottom row;1959-1969) was never fitted with the full-size units but many used slimmer version available from both the factory and third-party suppliers; again, in competition, spats in any shape were usually discarded.  On the big Jaguars, spats (which had already been scalloped) disappeared after production of the Mark IX ended in 1961.    

On cars, it wasn’t until the 1930s that spats (which some English manufacturers called "aprons" and in the US they came to be called “fender-skirts” though the original slang was “pants”) began to appear as the interest in streamlining and aerodynamic efficiency grew and it was in this era they became also a styling fad which, for better and worse, would last half a century.  They’d first been seen in the 1920s as aerodynamic enhancements on speed record vehicles and some avant-garde designers experimented with enveloping bodywork but it was only late in the decade that the original style of separate mudguards (later called cycle-fenders) gave way to more integrated coachwork where the wheel-arch was an identifiable feature in the modern sense.  Another issue was that the early tyres were prone to wear and damage and needed frequently to be changed, hence the advantage of making access to the wheels un-restricted.  In the 1930s, as streamlining evolved as both a means to reduce drag (thus increasing performance and reducing fuel consumption) and as a styling device, the latter doubtlessly influenced by the former.  On road cars, spats tended to be used only at the rear because of the need to provide sufficient clearance for the front wheels to turn although there were manufacturers (Delahaye, Nash and others) which extended use to the front and while this necessitated compromise (notably the turning circle and cooling of the brakes), there were some memorable art-deco creations.

The aerodynamic advantages were certainly real, attested by the tests conducted during the 1930s by Mercedes-Benz and Auto-Union, both factories using spats front and rear on their land-speed record vehicles, extending the use to road cars although later Mercedes-Benz would admit the 10% improvement claimed for the 1937 540K Autobahn-kurier (highway cruiser) was just “a calculation” and it’s suspected even this was more guesswork than math.  Later, Jaguar’s evaluation of the ideal configuration to use when testing the 1949 XK120 on Belgium roads revealed the rear spats added about 3-4 mph to top speed though they precluded the use of the lighter wire wheels and did increase the tendency of the brakes to overheat in severe use so, like many things in engineering, it was a trade-off.

1958, 1959 & 1960 Chevrolet Impalas.  Not actually wildly popular when new, accessory spats now often appear on restored cars as a “period accessory”.

In the post-war years, concerns with style rather than specific aerodynamic outcomes probably prevailed.  In the US especially, the design motifs borrowed from aircraft and missiles (where aerodynamic efficiency was important and verified in wind tunnels) were liberally applied to automobiles but in some cases, although they actually increased drag, they anyway appeared on production cars because they lent the desired look.  Because they added to the cost of production, spats tended often to be used on the more expensive ranges, this association encouraging after-market accessory makers to produce them, often for models where they’d never been available as a factory fitting or option.  Although now usually regarded as naff (at least), there’s still some demand because they are fitted sometimes (often in conjunction with that other acquired taste period-accessory, the "Continental" spare-tyre kit) by those restoring cars from the era although the photographic record does suggest that when the vehicles were new, such things were vanishingly rare.

Spats vanished from cars made in the UK and Europe except among manufacturers (such as Citroën) which made a fetish of conspicuous aerodynamics and in the US, where they endured, increasingly they appeared in cut-down form, exposing most of the wheel with only the upper part of the tyre concealed.  By the mid 1990s spats appeared only on some of the larger US cars (those by then also down-sized from their mid-seventies peak) and none survived into the new century, the swansong the 1996 Cadillac DeVille.  However, the new age of efficiency did see a resurgence of interest with spats (some actually integrated into the bodywork rather than being detachable) used on some electric and hybrid vehicles where every possible way of optimizing the use of energy is deployed.

1 1937 Mercedes-Benz 540K Autobahn-kurier
2 1937 Mercedes-Benz W125 Rekordwagen
3 1937 Auto-Union Type C Stromlinie
4 1939 Mercedes-Benz W154 Rekordwagen
5 1939 Mercedes-Benz T80 Rekordwagen
6 1940 Mercedes-Benz 770K Cabriolet B
9 1970 Porsche 917 LH
8 1988 Jaguar XJR9

1939 Mercedes-Benz T80, Mercedes-Benz Museum, Stuttgart, Germany.

Designed by Ferdinand Porsche (1875–1951), the Mercedes-Benz T80 was built between 1937-1939 to lay siege to the world land speed record (LSR) but with the outbreak of World War II (1939-1945), the attempt was never made.  It was a single-purpose machine designed to achieve maximum terminal velocity and for that reason, the T80 was an exercise in pure functionalism; not one nut or bolt was used other than for the purpose of ensuring its top speed would be as high as possible.  Cognizant of the existing record, the initial goal was 550 km/h (342 mph) but as others in the late 1930s raised the mark, so were Professor Porsche’s ambitions and when the final specification was set in 1939, the target was 650 km/h (404 mph) (not 750 km/h (466 mph) as is sometimes quoted).  Configured with six wheels, the T80 would have used a supercharged, fuel-injected, 44.5 litre (2716 cubic inch) Daimler-Benz DB 603 inverted V12 aero-engine, an enlarged version of the DB 601 which powered a number of Messerschmitts and other warplanes.  Intended for use in bombers, the T80’s engine was actually the third DB 603 prototype and was initially tuned to generate some 2237 kW (3000 horsepower) on an exotic cocktail of methyl alcohol (63%), benzene (16%), ethanol (12%), acetone (4.4%), nitrobenzene (2.2%), avgas (2%), and ether (0.4%) with MW (methanol-water) injection for charge cooling and as an anti-detonant.  This was more than twice the output of the Hurricanes, Spitfires and Messerschmitts which in 1940 fought the Battle of Britain but Porsche’s calculations suggested 2,574 kW (3,500 hp) would be needed to touch the 650 km/h target and the DB 603 would have been re-tuned to achieve this as an “emergency war rating”.

1939 Mercedes-Benz T80, Mercedes-Benz Museum, Stuttgart, Germany.

Some 8 metres (26 feet) in length with two of the three axles providing drive, the weight when fuelled and crewed was some 2600 kg (2.9 short tons) while the measured coefficient of drag (CD) was reported at 0.18, an impressive figure for such a thing as late as the 1990s and it would have been lower still, had wind-tunnel testing not revealed the need to add two small “winglets” to provide sufficient down-force to ensure the shape didn’t at speed assume the characteristics of an aeroplane and "try to take off" and notably, when in 1964 the Bluebird-Proteus CN7 set the flying mile record at 403.1 mph (648.7 km/h), it was the first LSR machine to include “ground effect” technology to reduce lift.  Fundamentally, the aerodynamics are thought sound although there would be the usual vulnerability to cross-winds, the cause of several deaths in such attempts and the surface conditions of what was a temporarily closed public road would also have been critical; whether the tyre technology of the time would have been adequate under such conditions will never be known.  Had the T80 been run on the long, flat straights of the salt flats in the US (Bonneville) or Australia (Lake Eyre), the prospects of success would have been better but for propaganda purposes (always a theme for the Nazis) the LSR runs had to be on German soil.

Bluebird-Proteus CN7, Lake Eyre, Australia, 1964.

The plan was for the attempt to be staged in January 1940 during what the regime dubbed RekordWoche (Record Week) on a section of the Berlin-Halle-Leipzig autobahn (now part of the A9), closed for the occasion.  The legend is that Adolf Hitler (1889-1945; Führer (leader) and German head of government 1933-1945 & head of state 1934-1945) himself choose the nickname Schwarzer Vogel (Black Bird) but that too may have been propaganda.  The design was all done in the era of slide rules and although some computer work has been applied to emulating the event, there’s no consensus on whether the T80 really would have hit 650 km/h and set the world land speed record (LSR).  As it was, it wasn't until November 1965 that the 650 km/h mark was reached by a machine powered by four fuel injected Chrysler 426 cubic inch (7.0 litre) hemi V8s.  On the Bonneville Salt Flats, it recorded a two-way average of 658.526 km/h (409.277 mph).

Ground effects: 1970 Chaparral 2J (the "sucker car"). 

The most extraordinary vindication of the concept was probably the 1970 Chaparral 2J, built for the Canadian-American Challenge Cup (the Can-Am, a series for unlimited displacement sports cars under the FIA’s minimalist Group 7 rules).  Although using a similar frame and power-plant (the all aluminum, 427 cubic inch (7.0 litre) Chevrolet V8 (ZL1)) as most of its competition, it differed in that the bodywork was rather more rectilinear, the transmission was semi-automatic and, most intriguingly, the use of two small auxiliary engines (Rockwell JLO 247 cm³ two-stroke, two-cylinder units which usually powered snowmobiles).  Unlike the auxiliary engines used in modern hybrids which provide additional or alternative power, what the Rockwells did was drive two fans (borrowed from the M-109 Howitzer, the US Army’s self-propelled 155 mm (6 inch) cannon) which pumped air from underneath at 9650 cfm (cubic feet per minute) (273 m3 per minute), literally sucking the 2J to the road, the technique enhanced by a Lexan (a thermoplastic polymer) skirt which partially sealed the gap between the shell and the road.  The rear spats (integrated into the body-shell) were part of the system, offering not only their usual contribution to reduced drag but increasing the extent of the suction generated by the extractor fans.  The 2J was immediately faster than the competition but the suction system proved fragile although, as a proof of concept it worked and it was clear that only development was needed to debug things.  Unfortunately, innovation and high speeds have always appalled the FIA (the Fédération Internationale de l'Automobile which has for decades been international sport’s dopiest regulatory body) and they banned the 2J.  Really, the FIA should give up on motorsport and offer their services to competitive crochet where they can focus on things like pins and needles not being too sharp.

1949 Delahaye 175-S Saoutchik roadster (left), 1967 Cadillac Fleetwood Sixty Special  (centre) & 2016 Rolls-Royce Vision Next 100 (electric) (right).

Fashions change and spats in the post-war years became unfashionable except in the odd market segment which appealed to an older demographic and even there, as the years were by, they were cut-away, revealing more of the wheel & tyre but they never entirely went away and designers with big computers now don’t even need even bigger wind tunnels to optimize airflow and spats have been displayed which are mounted vertically, some even responding to dynamic need by shifting location or direction.

Flown first in 1938 and named after the Spartan admiral Lysander (circa 467-395 BC), the Westland Lysander was a British army co-operation and communications aircraft used extensively during the Second World War (1939-1945).  Although it couldn’t match the extraordinary STOL (short Take-Off & Landing) performance of the its German contemporary the Fieseler Fi 156 Storch, it was capable, robust and had a good enough short-field capability to perform valuable service throughout the conflict.  Like many aircraft with a fixed undercarriage, partially enveloping spats were fitted to reduce drag but those on the Lysander had the unusual feature of being fitted with their own removable spats (similar to those used on automobiles).  Once these were dismounted, assemblies could be fitted to mount either Browning machine guns or stub wings which could carry light bombs or supply canisters.  The arrangement was popular with ground crew because the accessibility made servicing easy and pilots appreciated the low placement because the change in weight distribution had little adverse effect on handling characteristics.

Tumblehome

Tumblehome (pronounced tuhm-buhl-hohm)

(1) In naval architecture, an inward and upward slope of the middle body of a vessel; of the sides of a ship: To incline or slope inwards, to contract above the point of extreme breadth.

(2) A conceptually similar shape applied, in reverse, to the upper body of an automobile.

1828: A compound word, tumble + home.  Tumble was from the Middle English tumblen (to fall over and over again, tumble), frequentative of the Middle English tumben (to fall, leap, dance), from the Old English tumbian, from the Proto-Germanic tūmōną (to turn, rotate).  It was cognate with the Middle Dutch tumelen and the Middle Low German tumelen & tummelen.  Home was from the Middle English home, hom, hoom & ham, from the Old English hām (village, hamlet, manor, estate, home, dwelling, house, region, country), from the Proto-West Germanic haim, from the Proto-Germanic haimaz (home, village), from the Proto-Indo-European tḱóymos (village, home), from the root tḱey-.  The (rare and probably extinct) alternative spelling is tumble home.  Tumblehome is a noun; the noun plural is tumblehomes.

The meaning of the word tumblehome has been well understood from its first appearance in the early nineteenth century but the origin has never been obvious.  Shipbuilders had for centuries been using variations of the design for a number of reasons but the first known instance of the word dates only from 1828 and then without explanation, suggesting the term may already have been in common use, at least within the industry.  An 1848 reference from a shipwright does however hint at some sense of novelty, noting “… the upper works usually incline towards the middle line, or as it is termed “tumble home”.  The word “tumble” to refer to the sides of ships appears to have been used at least as early as 1687 but the compound tumblehome seems not to have emerged for another hundred and fifty-odd years.  The idea always summoned was of the imagery of the sides of a ship “tumbling down” the slope created but why “home” was added remains a mystery, the assumption being it was based either on (1) an association with certain domestic architectural styles of the time (2) the romantic notion of the sea, to which the tumblehome falls, being "home" for sailors or  (3) the idea of a dilapidated house in the throes of "tumbling down", fallen bits an pieces accumulating at the bottom.

Big ships and fast cars

In automotive design (upper), the term is applied when the width of the cabin (cockpit or glasshouse) reduces as the height rises.  Although curved glass in the side windows of cars began widely to be adopted in the mid-1960s, thus creating a mild tumblehome effect, the term is applied only when it is sufficiently severe to be apparent to casual viewers.

In naval architecture (lower), the geometry is reversed, a tumblehome define as a hull which flares out as the sides approach the waterline.  Although in some vessels, the effect is barely detectable by the naked eye, it’s a technical term and applies to all hulls which dimensionally qualify.  The opposite, the classic shape for ships’ hull, is called the flare.

USS Brooklyn, 1896.

Tumblehome, unless taken to extremes, was functional in that it improved stability in warships under sail; sailing ships heel (they tend to lean over when moving) and tumblehome reduced this.  At the time, the biggest contributor to a warship’s mass on the upper decks was the guns and a tumblehome design, moving the centre of gravity lower, allowed armament to be maintained or even increased without further loss of stability.  Additionally, there was the benefit of making it harder for boarding parties to climb aboard.  In commercial shipping, vessels were long taxed on the basis of the square footage of a ship’s deck and fat ships with a pronounced tumble carrying the same freight but taxed less, were attractive.  Government fiscal policy thus influenced and distorted design and engineering principles in the same way tax arrangements of windows affected architecture and those on cylinder bores (adversely) affected engine design.

Lamborghini LP500 Countach prototype, 1971.

The Countach had one of the most extreme implementations, the angle meaning it was possible for only part of the side-window to be lowered but at least the Italians were more thoughtful than the Germans; in 1954, facing a similar challenge with the side-glass on the 300 SL (W198 1954-1957) gullwing, Mercedes-Benz simply fixed the panes, ventilation provided only by small quarterlights.  Neither flow-through ventilation or air-conditioning was available so driving in a gullwing could be hot and sticky experience and there's a reason they're sometimes seen being driven (at low speeds and not on public roads) with at least one door open. .  The tumblehome is used by high-performance cars because of the aerodynamic advantages it confers, reducing frontal area an allowing the curve of the greenhouse to be optimized for air-flow, lowering resistance.  Because of great advances made during the late twentieth century, refinements to tumblehomes no longer deliver the 3-5% improvements in a drag coefficient (CD) which once was possible, engineers now pursuing factional gains.  The origins in cars however lay in the quest for more interior space and for mass-market vehicles, bulging out the sides gained the odd vital inch and the technique, combined with curved side glass, has become almost universal although there has been the odd deviation.  Stylists are predicting tumblehomes are likely to become more exaggerated as sides need to be bulkier to meet more rigorous side-impact regulations and roof-lines are lowered slightly in the quest to reduce drag.

Lindsay Lohan in tumblehome blonde wig.

What professional hair stylists call “the tumblehome” is a triangulated shaping which is most cases can’t be achieved without an expert application of product and when sported by models on photo-shoots, it’s common for the angles and an illusion of volume to be achieved with engineering no more complex than a sheet of cardboard (cut to suit) being attached with hairclips to the back of the head.  The look can however be achieved with synthetics which can be persuaded sustainably to behave in a way human hair naturally resists and Lady Gaga (b 1986) made a tumblehome wig a signature feature of her “Fame Monster” period (2009-2010).  With natural hair, a tumblehome with hair a little shorter than that of Lady Gaga’s wig is sometimes technically achievable given the right hair and a generous use of product the sideways projection would be noticeably less.

Lady gaga in Fame Monster mode.

The tumblehome style with the exaggerated elongations al la Gaga is rarely seen and usually represents a lot of work.  However, many take about as much effort to avoid the similar geometry of the “pyramid head”: a triangular shape with a flat crown area which flares to a wide bushy shape at the ends.  A function of length and weight for those with curly hair, pyramids happen usually when the strands are of almost uniform length and the curls tend to “stack”, the weight meaning the roots sit flattest on the scalp while towards the ends where the effective volume (hair + space) is greatest, the curled strands move sideways, unlike the behavior of straight hair which is purely downwards.

Lindsay Lohan with pyramid head, Saturday Night Live, 2004.

Stylists recommend layers as the best tactic to minimize the triangulation, the strategy essentially to create longer, diagonal layers to frame the face, meaning the remaining curls “sit into each other”.  What this does is simply physics, the layering on the surface reducing the weight, increasing the percentage of the volume on the crown area and although some are resistant, the best results will probably be achieved if the hair is cut dry because it will be presented at its natural weight.  When wet, the moisture content will disguise the extent of the left-right movement and exaggerate the up-down.  The shorter the layers of course the more effective the amelioration but this can be too radical for some so clients need to be turned into realists.

Dart

Dart (pronounced dahrt)

(1) A small, slender missile, sharply pointed at one end, typically feathered (or with the shape emulated in plastic) at the other and (1) propelled by hand, as in the game of darts (2) by a blowgun when used as a weapon or (3) by some form of mechanical device such as a dart-gun.

(2) Something similar in function to such a missile.

(3) In zoology, a slender pointed structure, as in snails for aiding copulation or in nematodes for penetrating the host's tissues; used generally to describe the stinging members of insects.

(4) Any of various tropical and semitropical fish, notably the dace (Leuciscus leuciscus).

(5) Any of various species of the hesperiid butterfly notably the dingy dart (of the species Suniana lascivia, endemic to Australia).

(6) In the plural (as darts (used with a singular verb), a game in which darts are thrown at a target usually marked with concentric circles divided into segments and with a bull's-eye in the center.

(7) In tailoring, a tapered seam of fabric for adjusting the fit of a garment (a tapered tuck).

(8) In military use, a dart-shaped target towed behind an aircraft to train shooters (a specific shape of what was once called a target drone).

(9) An act of darting; a sudden swift movement; swiftly to move; to thrust, spring or start suddenly and run swiftly.

(10) To shoot with a dart, especially a tranquilizer dart.

(11) To throw with a sudden effort or thrust; to hurl or launch.

(12) To send forth suddenly or rapidly; to emit; to shoot.

(13) In genetics, as the acronym DarT, Diversity arrays Technology (a genetic marker technique).

(14) Figuratively, words which wound or hurt feelings.

(15) In slang, a cigarette (Canada & Australia; dated).  The idea was a “lung dart”.

(16) In slang, a plan, plot or scheme (Australia, obsolete).

(17) In disaster management, as the acronym DART, variously: Disaster Assistance Response Team, Disaster Animal Response Team, Disaster Area Response Team, Disaster Assistance & Rescue Team and Disaster Response Team

1275–1325: From the Middle English dart & darce, from the Anglo-French & Old French dart & dard (dart), from the Late Latin dardus (dart, javelin), from the Old Low Franconian darōþu (dart, spear), from the Proto-Germanic darōþuz (dart, spear), from the primitive Indo-European dherh- (to leap, spring);.  It was related to the Old English daroth (spear), daroþ & dearod (javelin, spear, dart), the Swedish dart (dart, dagger), the Icelandic darraður, darr & dör (dart, spear), the Old High German tart (dart) and the Old Norse darrathr (spear, lance).  The Italian and Spanish dardo are believed to be of Germanic origin via Old Provençal.  The word dart can be quite specific but depending on context the synonyms can include arrow or barb (noun), dash, bolt or shoot (verb) or cigarette (slang).  Dart & darting are nouns & verbs, darted & dartle are verbs, darter is a noun, verb & adjective, dartingness is a noun, darty is a verb & adjective, dartingly is an adverb; the noun plural is darts.

Between the eyeballs: Crooked Hillary Clinton dart board.

The late fourteenth century darten (to pierce with a dart) was from the noun and is long obsolete while the sense of “throw with a sudden thrust" dates from the 1570s.  The intransitive meaning “to move swiftly” emerged in the 1610s, as did that of “spring or start suddenly and run or move quickly” (ie “as a dart does”).  The name was first applied to the small European freshwater fish in the mid-fifteenth century, based on the creature’s rapid, sudden (darting) movements (other names included dars, dase & dare, from the Old French darz (a dace), the nominative or plural of dart, all uses based on the fish’s swiftness.  The alternative etymology in this context was a link with the Medieval Latin darsus (a dart), said to be of Gaulish origin.  The name dart is now also used of various (similar or related) various tropical and semitropical fish.  It was in Middle English Cupid's love-arrows were first referred to as Cupid's dart (Catananche caerulea).  The modern dart-board was unknown until 1901 although similar games (the idea of archery with hand-thrown arrows) long predated this.  In zoology, the marvelously named “dart sac” describes a sac connected with the reproductive organs of certain land snails; it contains the “love dart” the synonyms of which are bursa telae & stylophore.  In archaeology, the term “fairy dart” describes a prehistoric stone arrowhead (an elf arrow).  A “poison dart” may be fired either from a dart gun or a blow-pipe (the term “dart-pipe” seems never to have been current) while a tranquilizer dart (often used in the management of large or dangerous animals) is always loaded into a dart gun.  The terms “javelin dart”, “lawn jart”, “jart” & “yard dart” are terms which refer to the large darts used in certain lawn games.  In the hobby of model aircraft, a “lawn dart” is an airframe with a noted propensity to crash (although it’s noted “pilot error” is sometimes a factor in this).  In military history, the “rope dart” was a weapon from ancient China which consisted of a long rope with a metal dart at the end, used to attack targets from long-range.

Making smoking sexy: Lindsay Lohan enjoying the odd dart.

The Dodge Dart

The original Dodge Dart was one of Chrysler's show cars which debuted in 1956, an era in which Detroit's designers were encouraged to let their imaginations wander among supersonic aircraft, rockets and the vehicles which SF (science fiction) authors speculated would be used for the interplanetary travel some tried to convince their readers was not far off.  The Dart was first shown with a retractable hardtop but when the 1956 show season was over, it was shipped back to Carrozzeria Ghia in Turin to be fitted with a more conventional convertible soft top.  After another trans-Atlantic crossing after the end of the 1957 show circuit (where it'd been displayed as the Dart II), it was again updated by Ghia and re-named Diablo (from the Spanish diablo (devil)).

1957 Dodge Diablo, the third and final version of the 1956 Dodge Dart show car.

Although a length of 218 inches (5.5 m) now sounds extravagant, by the standards of US designs in the 1950s it fitted in and among the weird and wonderful designs of the time (the regular production models as well as the show cars) the lines and detailing were actually quite restrained and compared with many, the Darts have aged well, some of the styling motifs re-surfacing in subsequent decades, notably the wedge-look.  Underneath, the Diablo’s mechanicals were familiar, a 392 cubic inch Chrysler Hemi V8 with dual four-barrel carburetors delivering power to the rear wheels through a push-button TorqueFlite automatic transmission.  Rated at 375 horsepower, the Hemi ensured the performance matched the looks, something aided by the exceptional aerodynamic efficiency, the CD (coefficient of drag) of 0.17 state of the art even in 2023.  Some engineers doubt it would return such a low number under modern testing but it doubtlessly was slippery and (with less hyperbole than usual), Chrysler promoted the Diablo as the “Hydroplane on Wheels”,  During Chrysler’s ownership of Lamborghini (1987-1994), the name was revived for the Lamborghini Diablo 1990-2001 which replaced the Countach (1974-1990).  Visually, both the Italian cars own something of a debt to the Darts of the 1950s although neither represented quite the advance in aerodynamics Chrysler had achieved all those years ago although the Lamborghini Diablo was good enough finally to achieve 200 mph (320 km/h), something which in the 1970s & 1980s, the Countach and the contemporary Ferrari 365 GT4 BB (Berlinetta Boxer) never quite managed, disappointing some.

The memorable 1957 Chrysler 300C (left) showed the influence of the Diablo but a more rococo sensibility had afflicted the corporation which the 1960 Dart Phoenix D500 Convertible (right) illustrates.  Things would get worse. 

Dodge began production of the Dart in late 1959 as a lower-priced full-sized car, something necessitated by a corporate decision to withdraw the availability of Plymouths from Dodge dealerships.  Dodge benefited from this more than Plymouth but the model ranges of both were adjusted, along with those sold as Chryslers, resulting in the companion DeSoto brand (notionally positioned between Dodge & Chrysler) being squeezed to death; the last DeSotos left the factory in 1960 and the operation was closed the next year.  Unlike its namesake from the show circuit, the 1959 Dodge Dart was hardly exceptional and it would barely have been noticed by the press had it not been for an unexpected corporate squabble between Chrysler and Daimler, a low volume English manufacturer of luxury vehicles which was branching out into the sports car market.  Their sports car was called the Dart.

Using one of his trademark outdoor settings, Norman Parkinson (1913-1990) photographed model Suzanne Kinnear (b 1935) adorning a Daimler Dart (SP250), wearing a Kashmoor coat and Otto Lucas beret with jewels by Cartier.  The image was published on the cover of Vogue's UK edition in November 1959.

With great expectations, Daimler put the Dart on show at the 1959 New York Motor Show and there the problems began.  Aware the little sports car was quite a departure from the luxurious but rather staid lineup Daimler had for years offered, the company had chosen the pleasingly alliterative “Dart” as its name, hoping it would convey the sense of something agile and fast.  Unfortunately for them, Chrysler’s lawyers were faster still, objecting that they had already registered Dart as the name for a full-sized Dodge so Daimler needed a new name and quickly; the big Dodge would never be confused with the little Daimler but the lawyers insisted.  Imagination apparently exhausted, Daimler’s management reverted to the engineering project name and thus the car became the SP250 which was innocuous enough even for Chrysler's attorneys and it could have been worse.  Dodge had submitted their Dart proposal to Chrysler for approval and while the car found favor, the name did not and the marketing department was told to conduct research and come up with something the public would like.  From this the marketing types gleaned that “Dodge Zipp” would be popular and to be fair, dart and zip(p) do imply much the same thing but ultimately the original was preferred.

Things get worse: The 1962 Dodge Dart looked truly bizarre; things would sometimes be stranger than this but not often.

Dodge got it right with the 1967-1976 Darts which could be criticized for blandness but the design was simple, balanced and enjoyed international appeal.  Two Australian versions are pictured, a 1971 VG VIP sedan (left) and a 1970 VG Regal 770 Hardtop (right).  

If Daimler had their problems with the Dart, so did Dodge.  For the 1961 model year, Dodge actually down-sized the “big” range, a consequence of some industrial espionage which misinterpreted Chevrolet’s plans.  Sales suffered because the new Darts were perceived as a class smaller than the competition, thus offering “less metal for the money”.  This compelled Chrysler to create some quick and dirty solutions to plug the gap but the damage was done and it was another model cycle before the ranges successfully were re-aligned.  However, one long-lasting benefit was the decision to take advantage of the public perception “Dart” now meant something smaller and Dodge in 1963 shifted the name to its compact line, enjoying much success.  It was the generation built for a decade between 1967-1976 which was most lucrative for the corporation, the cheap-to-produce platform providing the basis for vehicles as diverse as taxi-cabs, pick-ups, convertibles, remarkably effective muscle cars and even some crazy machines almost ready for the drag strip.  Being a compact-sized car in the US, the Dart also proved a handy export to markets where it could be sold as a “big” car and the Dart (sometimes locally assembled or wholly or partially manufactured) was sold in Mexico, Australia, New Zealand, the UK, Europe, East Asia, South Africa and South America.  In a form little different the Dart lasted until 1980 in South America and in Australia until 1981 although there the body-shape had in 1971 switched to the “fuselage” style although the platform remained the same.

How a Dodge Hemi Dart would have appeared in 1968 (left) and Hemi Darts ready for collection or dispatch in the yard of the Detroit production facility.

The most highly regarded of the 1967-1976 US Darts were those fitted with the 340 cubic inch (5.6 litre) small-block (LA) V8 which created a much better all-round package than those using the 383 (6.3) and 7.2 (7.2) big-block V8s which tended to be inferior in just about every way unless travelling in a straight line on a very smooth surface (preferably over a distance of about a ¼ mile (400 m) and even there the 340 over-delivered.  The wildest of all the Darts were the 80 (built in 1968) equipped with a version of the 426 cubic inch (7.0 litre) Hemi V8 tuned to a specification closer to race-ready than that used in the “Street Hemi” which was the corporation’s highest-performance option.  Except for the drive-train, the Hemi Darts were an extreme example of what the industry called a “strippers”: cars “stripped” of all but the essentials.  There was thus no radio and no carpeting, common enough in strippers but the Hemi Darts lacked even armrests, external rear-view mirrors, window winding mechanisms or even a back seat.  Nor was the appearance of these shockingly single-purpose machines anything like what was usually seen in a showroom, most of the body painted only in primer while the hood (bonnet) and front fenders, rendered in lightweight black fibreglass, were left unpainted.  Seeking to avoid any legal difficulties, Dodge had purchasers sign an addendum to the sales contract acknowledging Hemi Darts were not intended not as road cars but for use in “supervised acceleration trials” (ie drag racing).  Despite that, these were the last days that in the US one could find a jurisdiction prepared to register such things for street use and some owners did that, apparently taking Dodge’s disclaimer about as seriously as those in the prohibition era (1920-1933) observed the warning on packets of “concentrated grape blocks” not add certain things to the mix, “otherwise fermentation sets in”.

The warning: What not to do, lest one's grape block should turn to wine.