Units of Measure index

Other units


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This page describes some units that don't fit elsewhere on this website.
Speed - miles per hour, speed of light and sound, knot
Acceleration - g
Power - horsepower
Time
Intensity of light - candlepower
Comparisons

Speed

To convert between different units of speed, use this convertor below, which gives an answer rounded to 2 decimal places.

Enter speed:   =   ?  

The speed of an object describes how far something travels over a certain time. It is measured in distance/time. Speeds of people and vehicles are usually described as miles per hour or kilometres per hour, but metres per second and feet per second are used in Physics. In fact, the speed of light can be given as miles per second, to try to make a very large number a bit smaller.

Speed can be in any direction. Velocity gives not only the distance over time, but a direction as well.

British speed limits are still (2009) given in miles per hour. There is an example of a speed limit sign at the top of this page. 30 mph is the common speed limit for towns. This would be equivalent to 48.28 kilometres per hour. In United States of America, speed limits are also given in miles per hour, while in Canada, the limits are in kilometres per hour. Some Americans are apparently unaware of this, and assume that Canadians must drive very fast.

The speed of light in free space is a constant in all frames of reference (according to Einstein). It is 299,792,458 metres/sec, or (approx) 186,282.4 miles/sec.
The speed of sound is 343 meters/sec or 767 miles/hour. It is dependent on air temperature.
You can use the difference between these to see how far away a thunder storm is. See thunder storm.

A knot is a nautical measure of speed, one nautical mile per hour (or about 1.15 mph). The name comes from the knots tied in the log line used with the sand glass. The log line was thrown onto the sea and the knots in the line were counted as they ran out during the sand glass interval. The knot has been used since the 17c. It is sometimes called the sea mile. The international knot is very slightly less than the UK knot (as it is based on the international nautical mile). Click here for more information about the nautical mile.
I have been told by a correspondent:
"The knot : Two meanings. (Ignorance of this has led many "experts" into confusing others).
(a) Unit of speed = one nautical mile per hour. This is the normal definition today and comes, of course from the use of the Ship Log with its line marked (with a knot) every 47.3 ft or so and used with a sand glass.
(b) Unit of distance = one nautical mile. Conrad, that great stickler for correct nautical speech, uses both definitions as convenient. Context makes everything clear."


Acceleration

Acceleration is the rate of change of speed. If you put your foot down on the accelerator pedal, then you go faster, from one speed to a higher speed. If you brake, which is a negative acceleration, then you carry on going forward, but you slow down (and may stop).

The mass of the earth pulls stuff towards it. This is called gravity, and the acceleration due to gravity is constant at a given distance from the centre of the earth. So, on the surface of the earth, acceleration due to gravity (called g) is 9.80665 metres per second squared or 32.174 feet per second squared. In Physics lessons, you can do experiments to try to find g. When I was young, a group of us tried very hard to get the correct constant of 981 (this was the old metric system of centimetres per second squared). It wouldn't come right, but we tried hard, and figured in all sorts of experimental errors and eventually got close. The teacher looked at our work, roared with laughter, and told us that we were actually working in Imperial units and should be trying for 32 feet per second squared instead. Hm!


Power

Power is the amount of work done or energy transferred per unit of time.

James Watt invented the word horsepower to help market his improved steam engine, by comparing his engine to the work that a horse could do. There are different definitions of horsepower:

1 mechanical horsepower of 550 foot-pounds per second is equivalent to 745.7 watts.
1 metric horsepower of 75 kgf-m per second is equivalent to 735.499 watts.
1 horsepower for rating electric motors is equal to 746 watts.

Certain car names come from horsepower. The Austin 7 had an engine with capacity of 747cc which is estimated to generate about 7 horsepower. The Citroėn 2CV or Deux Chevaux was so-called because it was reputed to be only two horsepower, although there are a choice of engines and the smallest is 375cc.

The SI unit of power is the watt. It was named after James Watt (see above). A watt is one joule of energy per second.
The joule was named after James Prescott Joule, an English physicist. A joule is the work done by a force of one newton travelling through a distance of one metre.
The newton was named after Isaac Newton who discovered the laws of gravitation, reputedly after seeing an apple fall. A newton is about the weight of an apple. (Honestly!)

Here are some more convertors (answer rounded to 2 decimal places):

Enter fuel consumption:   =   ?  

Enter power:   =   ?  

Enter energy:   =   ?  


Time

People have always used natural phenomena to measure time, day and night, the moon, the sun. However, they have come up with different ways of doing this.

In modern times, all time measurement is based on the second, and this is defined in S.I. units as being the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom. This is a physical constant, and so well-defined. Not for everyday use, perhaps!

There are 60 seconds in a minute, and sixty minutes in an hour, making 3,600 seconds in an hour. This use of the number 60 dates back to Babylonian times, as they had a number system based on 60.

There are 24 hours in the day (or day and night), starting at midnight. In the past, the hours used to be described as am or ante meridiem (Latin for 'before noon') or pm or post meridiem (Latin for 'after noon'). Since midnight and noon could not be described that way, they had to be stated explicitly. Now we have the 24 hour clock. Use the convertor below if you can't do the conversions yourself, yet!

Convert between am/pm and 24 hour clock:  =  ?        =  ?

Houses of Parliament showing Big Ben

We are used to the times of day being the same in one time zone (such as throughout Britain). However, in the past, towns in Britain measured their hours according to the sun, so midday in one town would be a few minutes different from another. When the railways came, the rail companies needed to publish a single timetable which would work throughout Britain. So they created Railway Time (or Greenwich Mean Time), and all railway clocks showed it. If you wanted to catch a train, then your own clock had better run on Railway Time, and so this became standard time in Britain. Railway Time was first applied by the Great Western Railway in England in November 1840, and the rest of the rail companies followed them in the next few years. This page from an 1843 Bradshaw gives various local times in England, although it must been getting out of date by then.

The most famous clock in England is Big Ben. It is on the clock tower of the Houses of Parliament in London, built around 1859. The bells play part of the Westminster chimes on each quarter hour, gradually building up to the complete chime on the hour, after which the biggest bell (which is in fact Big Ben itself) strikes the hour. There is still a clockwork mechanism, which is adjusted by putting more or less old pennies on the pendulum.

It might be thought that the hours were always like this, but they weren't. The French revolutionaries tried to reform telling the time as well as other measurement. The day, from midnight to midnight, was divided into ten parts, each part into ten others, so on until the smallest measurable portion of duration. This system quickly went out of use, but some clocks still survive from that time (see right).

Even longer ago, the telling of the hours didn't begin at midnight. It started at dawn, and there were twelve hours during daylight. Since this day varied in length throughout the year, the hour varied too. The monastic timetable of the Benedictines had a regular round of services every 24 hours. Some of these were described by the hour. Prime was at day-break, or the first hour. Terce was the third hour, at about 9am. Sext was the sixth hour, at noon. None was at 3pm, the ninth hour.

The day is an obvious unit of time, which no-one seems to have any trouble with! As the earth turns, we are either facing the sun, daylight, or facing away from it, night-time.

French revolutionary clock

The next larger unit of time is the week. The Romans had an 8-day week, but the Christians had a 7-day week, like the Jews, and rested on the 7th day (except their day of rest is Sunday, rather than the Jewish Sabbath, Saturday). So once the Romans became Christian, they also adopted the 7-day week. In English the days of the week are named after the old Saxon gods, but French days of the week use Roman gods instead, and these correspond to the known planets and other heavenly bodies. Click here for more about the days of the week.

Once we get onto the month, things start to get complicated. The month is roughly based on a 'moon', or the time from one new moon to the next. Unfortunately, there is not an exact number of days in a moon (let alone a precise number of weeks), and there is not an exact number of moons in a year. Early calendars were lunar-based, and they found that this meant the start of the year, and all dates within the year, gradually changed when they happened compared with what the sun was doing. While moons are useful divisions of the year, what the moon is doing is not as important as what the sun is doing. You can't plant crops when the ground is frozen. There are still lunar calendars today. The Moslem calendar is used by Muslims everywhere to determine the proper day on which to celebrate Islamic holy days and festivals. It is a lunar calendar having 12 lunar months in a year of about 354 days. Because this lunar year is about 11 days shorter than the solar year, Islamic holy days, although celebrated on fixed dates in their own calendar, usually shift 11 days earlier each successive solar year. On the other hand, the Jewish calendar is a lunisolar calendar, or 'fixed lunar year' based on twelve lunar months of twenty-nine or thirty days, with an intercalary lunar month added seven times every nineteen years (once every two to three years) to synchronize the twelve lunar cycles with the slightly longer solar year. Each Jewish lunar month starts with the new moon. Although originally the new lunar crescent had to be observed and certified by witnesses, the timing of the new moon is now determined mathematically. Click here for more information about calendars used by different faiths.

The familiar January, February, March, etc. were invented by the Romans. Julius Caesar reformed their calendar so that the old 'moons' no longer corresponded with the real moon, although they were similar length. There were 12 months in a year, although of different lengths, and the new year started at the winter solstice (or in fact a few days after). The day lengths are described in this rhyme:

Thirty days has September,
April, June, and November;
All the rest have thirty-one,
Excepting February alone,
Except for February alone
And that has twenty-eight days clear
And twenty-nine in each leap year.
An easier way to work out the month lengths is given here. The old Roman year had started in March, which is why September, October, November and December are called the 7th, 8th, 9th and 10th month, when now they aren't! Click here for more about the months and their names.

Full moons fascinate people. The full moons throughout the year used to be given different names.

Old English names for full moons
SeasonFull Moon NameDate Range
WinterOld MoonJanuary
Wolf MoonFebruary
Lenten MoonMarch
SpringEgg MoonApril
Milk MoonMay
Flower MoonJune
SummerHay MoonJuly
Grain MoonAugust
Fruit MoonSeptember
AutumnHarvest MoonOctober
Hunter's MoonNovember
Oak MoonDecember

This website gives similar names to the Anglo-Saxon moons, except the first and last moons of the year were After Yule Moon and Before Yule Moon.

There may, of course, be more than one full moon in a month. There is a wide-spread belief that the second full moon in a moon is called a Blue Moon, which is used in the expression once in a Blue Moon, meaning very rarely. However, Sky and Telescope denies this. It says that if there are four moons in a season, the third one is the Blue Moon. This is based on American Farmers' Almanacs from the nineteenth and twenthieth century. I suspect that the expression is an American one. In Britain, in a blue moon sometimes means never! I would disagree with the allocations of the seasons anyway. June is obviously summer, and December is winter. As for the other moon names, I have heard of Harvest moon, but it seemed to be used of any large orange full moon in the autumn. I was told that the dust from the harvest would change the colour of the moon. And a hunter's moon meant a frosty bright white moon in the winter. It's interesting that this has been brought up to date. In the second World War, a bright full moon was described as a bomber's moon. The Germans were bombing Britain at night, and a good full moon helped them to be accurate. (Everywhere was dark, as the black-out turned off or concealed all lighting.) I don't know if it was also used to describe the British bombing the Germans.

A year is the length of time for the earth to travel round the sun. The earth's axis is tilted, so unless you're near the equator, you are slightly further away from the sun during half the year, winter, than the other half, summer. The sun's rays have to travel through more atmosphere during winter, and the day length is shorter. All this makes it colder. Since it is important to plant crops at the right time of year, it is important to know when the times of the different times of the year are. It is thought that one of the functions of Stonehenge was to find out when the winter solstice was. Even today, we are very careful to make sure that each year is precisely the right length. This is not as easy as you might think. If you add up the days in the months in a year, the total is 365 days. But the true length of the year is 365¼ days. To overcome this problem, an extra day is added to the end of February every 4th year, or leap year. However, even this is not enough, since the true length of the year is slightly less than 365¼ days. So years that are divisible by 100 are not leap years, unless they are also divisible by 400, in which case they are leap years. The last year divisible by 100 was 2000, which was divisible by 400, so that was a leap year.

The day is not quite a whole multiple of seconds. The adjustment is very small, but sometimes there has to be a leap second, a second added to the year to make it the right length. This is done at midnight either at the start of the new year or half way through the year. It happened at the start of 2009. Theoretically, a second could be subtracted instead, but this hasn't happened yet.

The months keep the same whether you're north or south of the equator, even though this means that Australia has January in the middle of the summer. However, everyone wants midnight to be in the middle of the night. But as the earth turns, the middle of the night happens at different times in different places. So there are different time zones. The base time zone is GMT or Greenwich Mean Time. Greenwich Observatory is in London, on the River Thames, and 0° longitude goes through it. There are different time zones throughout the world, so if you travel far enough, you have to adjust your clock (and if you cross the date line at roughly 180°, your calendar as well). Britain is on GMT during the winter, and what we call summer time during the summer, so we have to change our clocks each spring and autumn (and complain bitterly about it every time!) The formula for changing the clocks, by the way, is "Spring forward, fall back". This is probably an American expression (since we talk about autumn rather than spring) but it still works. At one point in the 20C, Britain operated on summer time during the winter, and double summer time during the summer. People still remembered about GMT, so they called GMT God's time, the summer time was Government time, and the double summer time was Daft time!

Christmas is always on December 25th, which is just after the winter solstice (the shortest day of the year). Easter varies through the year. Here is a 'Rhyme for remembering the Date of Easter' by Justin Richardson.

No need for confusion if we but recall
That Easter on the first Sunday after the full moon following the vernal equinox doeth fall.
Not very memorable! But accurate. The equinox is when days and nights are of equal length, and the vernal equinox is in Spring, around the end of March. The full moon can be immediately after, or up to four weeks after, and you may need to add up to a week after that, which explains why Easter jumps around so much.

One point worth mentioning perhaps - the British write a date in numbers as DD/MM/YY, while the Americans write MM/DD/YY. This can sometimes be ambiguous, so if you're travelling between the cultures, watch out! Some British may not have realised that 9/11 was a date in September (and our emergency number is 999 anyway, so more confusion).

Since months were originally based on the moon, and year length on the sun, it can be difficult to reconcile the two, which explains the different month lengths of our calendar. This can make it difficult to work out how many days there are between two dates. So here is a convertor (I'm putting day before month, because I'm British, OK?):

First date:Day Month Year Result:
Second date:Day Month Year

This convertor may not always be accurate. It copes with leap years when the year is divided by 4, and knows 2000 was a leap year while 1900 wasn't (did you know that?) But other divided-by-4 non-leap years are not covered. Nor does it deal with the change from Julian to Gregorian calendar, or BC years, because that would be silly. And it may not be accurate to a day, although I hope it is! But it should tell you how many days between two dates. Roughly.

There are different ways to number years. Christians number years from the birth of Jesus (although scholars think they may be a few years out). The millennium was celebrated in 2000 throughout the world (although some people think it should have been 2001 instead) despite the existence of other year numbering systems. Click here for more information about calendars used by different faiths.

The Chinese have a cycle of 12 years named after animals. The Chinese New Year starts in January or February. Recent years were:
NameStarted
Tiger1998 January 28
Rabbit1999 February 16
Dragon2000 February 5
Snake2001 January 24
Horse2002 February 12
Sheep2003 February 1
Monkey2004 January 22
Rooster2005 February 9
Dog2006 January 29
Pig2007 February 18
Rat2008 February 7
Ox2009 January 26
Tiger2010 February 14
Rabbit2011 February 3
The order starts with the rat. There is a story explaining this. Supposedly, the twelve animals fought over the precedence of the animals in the cycle of years in the calendar, so the Chinese gods held a contest to determine the order. All the animals lined up on the bank of a river and were given the task of getting to the opposite shore. Their order in the calendar would be set by the order in which the animals managed to reach the other side. The cat wondered how he would get across if he was afraid of water. At the same time, the ox wondered how he would cross with his poor eyesight. The calculating rat suggested that he and the cat jump onto the ox's back and guide him across. The ox was steady and hard-working so that he did not notice a commotion on his back. In the meanwhile, the rat sneaked up behind the unsuspecting cat and shoved him into the water. Just as the ox came ashore, the rat jumped off and finished the race first. The lazy pig came to the far shore in twelfth place. And so the rat got the first year named after him, the ox got the second year, and the pig ended up as the last year in the cycle. The cat finished too late to win any place in the calendar, and vowed to be the enemy of the rat forevermore.

I seemed to have wandered some way from Imperial units! But there are now many cultures that are part of Britain, and it's interesting to find out about them.


Intensity of light

The English standard for luminous intensity was candlepower. One candlepower was the light produced by a pure spermaceti candle weighing one sixth of a pound and burning at a rate of 120 grains per hour.

The SI unit is the candela. This is one of the SI base units. A candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 x 1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.


Comparisons

People like to compare measurements to other things, to make it easier to understand them. We have already met some units of area such as the 'size of Wales'. Here are some more:
length of double-decker bus
area of a football pitch
volume of a swimming pool
tastes like chicken
consistency of porridge

The 'porridge' consistency is courtesy of the TV programme Victorian Farm, who said that workmen seemed to use it a lot, e.g. to describe how to mix plaster.