Q & A: More speed, more effort . . . . . in running and penalties

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What is the least number of league appearances made by a footballer before his full international debut?

Nil. Len Evans (goalkeeper) played for Wales against Scotland and England in 1930 before making his league debut for Cardiff City. Steve Heighway played for the Republic of Ireland against Poland in 1970 before his league debut for Liverpool. Both these 'debutants' did not play in a winning side - obviously a moral here somewhere. In more recent times it appears that half a decent season for Arsenal guarantees an England cap. - Tim O'Brien, London E5.

Don Givens won two caps for the Republic of Ireland before his debut for Manchester United in 1969. Gary Charles played in only 20 league games before his England debut in June 1991 - 12 for Nottingham Forest and eight on loan to Leicester City. Of these, only 15 were full appearances; the other five were as substitute.

Because of the suspension of league football during the war, several of the England side against Northern Ireland in September 1946 had only made a handful of league appearances - Henry Cockburn, for instance, had only played seven matches for Manchester United. - Michael Crick, Chipping Norton.

I understand that, in terms of population, Aldershot was the smallest town to support a Premier/League football club. Since their demise, what is now the smallest town to support a League club. Conversely, what is the largest town which does not have League representation?

No mention seems to have been made of Workington. The population of the Cumbrian town is only 26,000 but Workington AFC was a member of the Football League for many seasons and under managers as distinguished as Bill Shankly, Joe Harvey and Ken Furphy. - W N Cockburn, Liverpool.

Re Wakefield's non-representation in the the Premier or Football League (Q&A, 6 Dec), I thought the following details might be of interest.

On 7 March 1921, the Northern Section of the old Third Division was formed, and after the first 16 candidates had been admitted it was found there were four vacancies, for which the voting was as follows:

Wigan Borough34 votes

Halifax Town25

Southport Central25

Stalybridge Celtic25

All elected

Castleford Town18

Rotherham Town13

Blyth Spartans9

Gainsborough Trinity8

Doncaster Rovers6

West Stanley6

WAKEFIELD CITY4

Lancaster Town3

Scunthorpe3

South Liverpool1

So that was the nearest Wakefield ever reached in connection with membership of the Football League - seventh in the list of unsuccessful candidates. - L Burgess, London N2.

If it takes me four hours to run a marathon, am I working harder than someone who can run the distance in two and a half hours? How do you quantify effort?

When you are running on level ground, the resistance depends on the ground resistance, which remains roughly constant, and the wind resistance. The wind resistance depends on your frontal area, the density of the air, the speed and the Cd - drag coefficient.

The power needed to overcome the air resistance is proportional to the cube of the speed. A person who completes the marathon in two and a half hours, rather than four hours, will be producing power at the rate of (4 divided by 2.5)3 .

This works out as a little over 4. So the faster athlete will be working four times as hard.

And the question is, what is the power of an athlete. Many years ago, when people were competing for the Kremer prize, to build a man-powered aircraft, measurements were done to find how powerful an athlete was - and they came to the conclusion that for a short time, a fit male athlete could sustain about one and a half horse power for a short time.

The actual wind drag increases as the square of the speed. So the athlete completing the race in 2.5 hours rather than 4 will experience a force (4 divided by 2.5)2

This works out as just over two and a half times as big a force. But it is easy to come out with all sorts of formulae. Horses rarely work at a real horse power, drag coefficients vary depending on whether an athlete is wearing a shiny track suit, or a bare chest. If you run in the hills, where air density is lower, the wind resistance will be less, but you may have difficulty breathing. - Robin Cooper, St Alban's.

Two identical athletes will expend the same amount of energy in conveying themselves over a given distance, regardless of their respective times. Power is a measure of the rate at which energy is expended, and therefore the athlete who finishes first will have developed a greater power, and will have worked harder. - Vince Hammond, Leeds.

I ran the London Marathon this year. It took me 4hr 31min and it was b----- hard work. - Andrew Kirkham.

It has always been my contention that if a goalkeeper facing a penalty kick does not move until the ball is struck and the ball is kicked hard to the corner of the goal it will be impossible for him to make a save. Is this true?

The answer here is purely a matter of anatomy. The human body cannot be propelled downwards nearly so powerfully and quickly as it can be upwards. There are no large muscle groups which can do the former but several which can do the latter. Consequently, the main force involved in getting us to the ground is gravity.

A football struck to the keeper's side at anything above chest level can be reached by him using his powerful thigh muscles and the extension of his arms. Anything higher than that is generally easy to reach, provided it is not too much to his side (witness the number of shots tipped over the bar).

I have memories of a trial conducted some years ago, in which the goalkeeper was forbidden to move until the ball was struck (which is the rule, after all). Balls were kicked from the spot quickly but firmly along the ground into a corner net.

It was proved conclusively that in these circumstances it is impossible for the human frame to get to the ball in time. Not one was saved.

Johnny Hubbard, a South African who played for Glasgow Rangers n the Fifties, was the past-master at this. He was the regular penalty taker for the 10 years he was of Ibrox, and he missed only two] Considering he could have taken, say, 200 or more, I think the point is made. - Dr F W G Deighton, Glasgow.

Who is the heaviest man to have played first-class rugby?

Philip Rudolph 'Flippie' van der Kerwe made six appearances for South Africa between 1981 and 1989 and at the time of his first cap he weighed 132kg (20st 10lb). In April 1986 he played for an Overseas XV against a Five Nations XV at Twickenham. The match programme gives his weight as 22st 2lb.

Norm Hadley, who played for the Barbarians against Australia at Twickenham last month, weighs 19st 8lb. - John M Jenkins, Bow Street, Dyfed.

ANSWERS PLEASE

Why is a match between local rivals referred to as a 'derby'? - Jeremy Hudson, Chester.

As a Leeds United fan I hate to tempt fate, but has a championship-winning side ever been relegated the subsequent season? - Alan M J Bush, Cheltenham.

Has there ever been an occasion in cricket where a hat-trick has been performed with the first three balls of a match? - Mr A C Preston, Stockport.

In football, why are goalkeepers no longer penalised for taking more than four steps while holding the ball? What should the penalty be? - Marie MacDonald, Pinner.

Can anyone tell me which first-class cricketer holds the record for the most consecutive games in both county championship and one-day cricket? - Paul Parry, Ashby de-la-Zouch.

Has any professional footballer ever held a PhD or other higher degree (not including those awarded on an honorary basis)? - David Bell, Hexham.

Why do English rugby union supporters sing the negro spiritual 'Swing Low, Sweet Chariot'? - Margo Fraser, Edinburgh.

What is the area of the human foot used by athletes when they run? Is it the ball of the foot that lands first or the heel? - Douglas B Ellison, London SE16.

Since the introduction of three points for a win, have more matches ended in home wins than before? - Nicholas E Lane, Bristol.

If you know the answers to any of these questions, or have a sporting question of your own you would like answered, write to:

(Photograph omitted)

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