Robin Hood Give Us Your Best Shot!!!!!!!

Mathspig went along to see the movie, ROBIN HOOD, starring Russell Crowe and Cate Blanchett. I was interested in the film for several reasons.

Firstly, Cate Blanchett went to the same primary school as Mathspig’s children in Melbourne. Such is our Aussie egalitarian attitude to education we do not single out past students for special attention.  No picture of Cate Blanchett appeared at the school during Mathspig’s kids education and none, as far as I know, to date.

Secondly, I’m amused that two Australian stars featured in an American remake of a British classic tale. I was just a bit disappointed that Russell Crowe didn’t say something like ‘No worries, King John, mate!!!!

Another amusing aside was that the re-engineered history in this Ridley Scott tale meant Robin Hood had a great influence on British History. I am only too delighted to discover that Russell Crowe wrote the Magna Carta.

How Far Could Longbow Men shoot their Arrows?

I was very intrigued by how the long bowmen fired their arrows. Robin Hood begins the film as a long bowman called Robin Longstride. The film critic for the New Yorker suggested ‘Longstride’ was not the ideal name for Russell Crowe’s nuggetty Robin. I think Robin Chunky-Guy might be more appropriate.

When I did some research ( Longbow arrow speeds)I found that Russell Crowe’s build was closer to the original longbow men than earlier Robin Hoods such as the tall and rangy Errol Flynn (Shown).  It is believed that longbow men of the era could draw -a force (on the bow string) of 150 lb-f (pound force) or 667 N (Newton), which is, at least, twice the draw force of bowmen today who, if they are good, can draw 60 – 80 lb-f or 267 – 356 N.

Longbow men used heavy wooden arrows and not the carbon shafts used by archers today. Arrow speeds are estimated for the longbows to be up to 310 f/s (foot per sec) or 100 m/sec.

In the film I noticed that Robin Hood – especially in one dramatic shot at the end, – aimed his arrow at a high angle in the air. ( See Below)

Mathspig believes you should always find the easiest way to do any calculation. so here is the EASY way. Assuming there is no wind or wobbly arrow movement we can split the arrow velocity into its horizontal and vertical components (Using vectors. If you haven’t done vectors just go along with it.) Then interesting things happen!!!!!!!!

 

We haven’t allowed for air resistance in the flight of the arrow so it would slow down….. BUT Russell Crowe … I mean ROBIN HOOD was right.AIM HIGH and your arrows go a long, long way!!!!!!! Of course, the straight arrow traveling at 100 m/sec would travel 1000 m in 10 seconds or 1 km!!!!!! 

Mathspig finds this amazing.

Sharp Shooter Maths

Mathspig grew up on a police station in the small Australian country town of Kyneton, Victoria in the 1960s. Mum fed the prisoners. Dad’s car an old FC Holden, maroon and white with a pink door, was the police car. And the police phone sat in the kitchen.

Australia has a very strict gun laws today. Thank goodness. But such laws didn’t exist in the sixties. My Dad’s .22 rifle rested against the fridge in the kitchen – without it’s 6-bullet magazine – in case my dad was called out to some police emergency.

There were a number of gun incidents in my childhood. One time my mum was cleaning the house. She usually put paper rubbish in her apron pocket and threw it at the end of the day into our combustion (wood-fired) stove. She forgot she had three .22 bullets in her pocket. It took some time for the bulletsto heat up.

My parents were in bed when bullets started exploding in the kitchen. The explosion blew off the hot plate and blew the ash door open covering our kitchen in grey ash. And it nearly gave my dad a heart attack. This was a typical story of my childhood and why I became a humour writer.

My Dad the Sharp Shooter My dad stopped a stolen car with one bullet. This was considered legendary by his fellow cops. He didn’t shoot the tyres. He managed, by accident and possibly even though he was aiming at the tyres, to hit the electrical lead into the car’s  distributor cap. Phht! Car go no more.

Sharp Shooter Maths

 One measure of the accuracy of rifles, riflescopes but also the sharpshooter is the MOA or Minute of Angle.  The MOA can also be used to define the target zone (circle).

I cannot show you a triangle with an angle of 1′ because it would have to be 100m long on one side and only 3cm tall or 100 yds long and approx 1 inch tall.

Needless to say, drawings are NOT to scale.

A sharpshooter can put 5 out of 6 bullets in a target zone drawn at 1′ angle around centre of target at any distance.

(See pics. )

As the distance away from the target increases the target zone circle area increases.

When Mathspig recently saw images of some Russian soldiers covered in medals it prompted the question ‘Would medals protect the wearer from a sharpshooter?’ Note: Mathspig has obscured the identities. This is a theoretical maths question. 

Mathspig was interested in this question because megalomaniac military dictators who take over countries by force tend to award themselves lots of medals. But they are also likely to be the target of sharpshooters from a liberation movement.

The diameter of a standard military medal is 3.5 cm. Mathspig has drawn up a diagram with loosely packed medals.

Using Pythagorus Theorem we can calculate the distance ac and then by subtracting 2r (2 x radius of the medals) we end up with the diameter n of the target zone circle.

Even at 100m the sharpshooter is looking at a target zone circle with a radius of 0.46cm. That is less half cm!!!!!!! The target zone is less than the size of an American Quarter and about the size of an Australian 10 cent coin or a British Pound. This is very difficult.

At 100m the sharpshooter is doing well to hit target in a target zone circle of 2.91 cm.

At 200m the target zone circle radius is 5.81 cm.

So the megolmaniac military dictator wins!!! He IS protected – on his chest – by his medals!!!!!! Unless the sharpshooter manages a ‘lucky’ shot.

Another way to look at the sharpshooter problem would be to calculate the MOA – or minute of angle- to get inside the target zone.  Here are the calcs for 200m. Find WEB 2.0 Scientific Calculator handy here.

Make me feel real loose like a long legged goose!!!

Everyone knows that women’s magazine editors digitally alter photographs of models that appear in their mags. When I finally did the maths I was shocked.  See: Odd Bods in Marie Claire

This model had legs 89% longer than a standard size 12 model in the same edition of the magazine and with the same waist to hip measurement! Looking at this model made the standard size 12 model look like a dumpy little garden gnome. Looking at these images distorts our view of normal body sizes or anything close to it.

Models can be given the appearance of long legs by the angle of the camera (Looking up at the model on the catwalk, for instance), by wearing extra high stiletto heels and/or by wearing bathing costumes with high cut legs. Then photo editors use photoshop to stretch their legs.

While pictures of male models may be digitally altered to remove skin blemishes, body hair and add abs, it seems to me that their legs are not digitally stretched and certainly not by 89%! But we have this 89% number now and we should use it.

So Mathspigs here are some male celebrities with a standard pic and then with their legs – from the hip down – stretched by 89%.

This was very simple maths. I used photoshop to edit the pictures and set their legs at a 189% vertical stretch. 

Check the maths:

Standard leg length = 100%

Vertical Stretch        = 89%

FINAL LEG LENGTH  = 189% 

Look at these pics and you decide if they look OK or ridiculous. I cannot decide for you. But I have thrown in the pics of the horse and the giraffe just to show how the practise of digitally stretching models images distorts reality. 

Here we go mathspigs. Lets play STRETCH LIMBO!!!!!!!!!!!!!!!!!!!!!!!!!!

Zac Efron

Maybe these

long legs would

help his

dancing, but…..  if he did the splits he’d never get up again.

Robert Pattison

plays

Edward Cullen

in the Twilight series. See TWILIGHT MATHS II

Edward is an ethical vampire

at this height he’d have to chase giraffes.

Justin Beiber

As my photoshop leg stretching skills improved

I found that

our eye begins to accept legs stretched

from the top of the thigh but not higher up the body.

Check out these stretch-horses.

Both images have legs stretched by

89% but the second horse has been stretched from the mid-body point down. Now look at the normal horse. It looks like it has SHORT legs!!!!!!! These images have distorted our sense of reality.

Here are some sports stars.

Sam Gilbert plays Aussie Rules football 

for ST KILDA.

PS: Mathspigs dad and two Uncles played for St Kilda.

My Dad broke his leg when he ran into the goal post. 

They sent him off to hospital using the local bus!!

This was along time ago.

My dad

and

two uncles

are in the

St Kilda team

photo 

together

in

1946.

Heath Grundy 

plays 

Aussie Rules 

Football 

for 

the 

Sydney Swans.

 

 Usain Bolt

 We would like to believe that Usain Bolt has long,

long legs.

 However he doesn’t need legs as long as the stretch photo suggest.

He is already the world’s fastest runner.

 

  The giraffe looks quite reasonable with extra long legs.

 Then again you could argue that

the real giraffe shape

is weird.

-

Now for a few rock stars.

 This is Vampire Weekend.

 The long Weekend is  Left.

-

Here is CUT OFF YOUR HANDS. 

Cut Off your Hands UNCUT is Right.

-

 This is the rock group GRIZZLY BEAR.

Look at the way our eye works.

Look at the guy in the shorts. His leg has been extended from the knee down. Looks wrong.

The guy in the black pants legs look OK even though extended 89%.

The guy squatting is totally distorted as his whole body and head have been stretched.

 Now you’ve seen a horse, a giraffe and a grizzly bear. 

Finally, a bit of fun.

Here are some fictional characters. 

Harry who???? The batman toy looks appears in proportion mainly because action figure toys are usually made with short muscly legs.

 

  - I used the standard 89% stretch here. I was hoping to give Spiderman legs like a spider.