Energy to Orbit vs Launch into Deep Space
insight

Energy to Orbit vs Launch into Deep Space

This is from Sanjoy Mahajan's The Art of Insight Problem 1.11 Estimate the energy in a 9-volt battery. Is it enough to launch the battery into orbit? I tried to answer this with the energy density required to launch into deep space. But this is different to going into orbit; how much energy is required to get into low Earth orbit? Low Earth Orbit A low orbit has to be above the height of the atmosphere (otherwise will require propuslion to overcome atmospheric friction), and so is typically above 300 km.

  • Edward Ross
Energy Desnsity to Launch into Space
insight

Energy Desnsity to Launch into Space

This is from Sanjoy Mahajan's The Art of Insight Problem 1.11 Estimate the energy in a 9-volt battery. Is it enough to launch the battery into orbit? I have already (mis)estimated the energy of a battery, but looked it up as 500 mAh. Energy density required to launch into space To launch into space you have to exchange energy to counteract the change in gravitational energy (at least, you'll need more for air resistance).

  • Edward Ross
Population Density Australia
insight

Population Density Australia

How dense is the population in Australia? I've looked at the Gridded Population of the World and you can see that the population is concentrated around the few capital cities on the coast. It's hard to visually average something so lumpy, but it's easy to estimate it. I know it's about 10 hours driving from Melbourne to Sydney, and about the same again to Brisbane. Brisbane is about halfway between Melbourne in the south and Cairns in the far north.

  • Edward Ross
Australian Deathographics
insight

Australian Deathographics

I've recently tried to estimate Australian Deaths using life expectancy. This failed badly and I think the reason is demographics; this article looks more into this. The Australian Bureau of Statistics has population by age, and the Australian Institute of Health and Welfare have Mortality Over Time and Regions (MORT) which summarises the current probability of death by age range. Here is a super summarised version of this data: Age Population Death Rate Population Deaths Fraction of Deaths 0-19 25% 0% 0% 0% 20-39 29% 0% 0% 0% 40-59 25% 0% 0% 0% 60-79 17% 1.

  • Edward Ross
Checking Australian Oil Imports
insight

Checking Australian Oil Imports

I've estimated Australian oil imports; here I check the data to see how reasonable my estimates are. The overall tree diagram for the estimate is below: graph BT; Import[Oil imports1.3 Million Barrels/Day] ImportL[Oil imports200ML/Day] -- Import Barrel[Size of Barrel160L] --|-1| Import Consumption[Oil consumed L/Day200ML/Day] -- ImportL ImportRatio[Oil Imported / Consumed1] -- ImportL CarConsumption[Oil Consumed by Cars100ML/Day] -- Consumption CarFraction[Oil Consumed in Total / Oil Consumed by Cars2] -- Consumption Cars[Number of Cars20 Million] -- CarConsumption ConsumptionCar[Oil Consumed by Car5L/Day] -- CarConsumption People[Number of People25 Million] -- Cars CarPeople[Number of Cars per Person0.

  • Edward Ross
Australian Oil Imports
insight

Australian Oil Imports

This is a variation of Sanjoy Mahajan's The Art of Insight Section 1.4 (and problem 1.6) How much oil does Australia import (in Barrels per Day)? As in the text we approach this by estimating car consumption. graph BT; Import[Oil imports Barrel/Day] ImportL[Oil imports L/Day] -- Import Barrel[Size of Barrel L] --|-1| Import Consumption[Oil consumed L/Day] -- ImportL ImportRatio[Oil Imported / Consumed] -- ImportL CarConsumption[Oil Consumed by Cars L/Day] -- Consumption CarFraction[Oil Consumed in Total / Oil Consumed by Cars] -- Consumption Cars[Number of Cars] -- CarConsumption ConsumptionCar[Oil Consumed by Car L/Day] -- CarConsumption People[Number of People] -- Cars CarPeople[Number of Cars per Person] -- Cars To estimate imports we estimate demand, since that is estimable.

  • Edward Ross
How many People in Australia Die?
insight

How many People in Australia Die?

How many people die in Australia each year? The life expectancy in Australia is about 80 years, and the population is 25 million. So each year the number of people that die would be about 25 million divided by 80, which is about 300,000. The actual number of people that died in 2018 is 160,000. This is about half my estimate; what am I doing wrong? One factor is life expectancy is at birth, the longer people live the longer they will be expected to live.

  • Edward Ross
Checking Australian Births Estimates
insight

Checking Australian Births Estimates

I estimated the number of Australian births as 250,000. The actual number of births, according to the Australian Institute of Family Studies, it's around 310,000. Where did I go wrong? My estimate was 25 million times 0.8 children per person lifetime divided by lifetime of 80 years. The actual total fertility rate is 1.74 per woman, giving a birth rate of around half this of 0.87 per person which is significantly higher than I estimated.

  • Edward Ross
Australian Births
insight

Australian Births

How many babies are born in Australia? Australia has 25 million people. I would estimate the birth rate is 0.8 children per person; I think it's slightly less than one. These children are born across life, which is about 80 years. So a really crude estimate for annual births is 25 million people times (0.8 children per person lifetime) divided by 80 years per lifetime. This is 20 million divided by 80 which is 250 thousand.

  • Edward Ross
Tree Diagram Bills
insight

Tree Diagram Bills

This is from Sanjoy Mahajan's The Art of Insight Problem 1.5 Make a tree diagram for your estimate in Problem 1.3. Do it in three steps: (1) Draw the tree without any leaf estimates, (2) estimate the leaf values, and (3) propagate the leaf values upward to the root. This is referring to the suitcase of money. Step 1: Tree graph LR; VolBankNote[Volume of Bank Note] VolSuitcase[Volume of Suitcase] ValueBankNote[Value of Bank Notes in Suitcase] NumBankNote[Number of Bank Notes in Suitcase] ValueSuitcase[Value of Suitcase] NumBankNote -- ValueSuitcase ValueBankNote -- ValueSuitcase VolBankNote --|-1| NumBankNote VolSuitcase -- NumBankNote SuitWidth[Width of Suitcase] -- VolSuitcase SuitHeight[Height of Suitcase] -- VolSuitcase SuitDepth[Depth of Suitcase] -- VolSuitcase BankHeight[Height of Bank Note] -- VolBankNote BankWidth[Width of Bank Note] -- VolBankNote BankDepth[Thickness of Bank Note] -- VolBankNote Step 2: Annotated Leaves graph LR; VolBankNote[Volume of Bank Note] VolSuitcase[Volume of Suitcase] ValueBankNote[Value of Bank Notes in Suitcase

  • Edward Ross
Mixing Warm Water
insight

Mixing Warm Water

I used to have a fancy kettle that came with settings for heating water to different temperatures between 80° C and 100° C. However it's really easy to get water at any temperature using an ordinary kettle by mixing with refrigerated water. When you mix together two volumes of water at different temperatures their volumes add and the resulting temperature is a volume weighted average of the temperatures. For example if you take 25mL of water at 10° C and 75mL of water at 40° C you will get 100mL of water at 32.

  • Edward Ross
Gold or Bills
insight

Gold or Bills

This is from Sanjoy Mahajan's The Art of Insight Problem 1.4 As a bank robber sitting in the vault planning your getaway, do you fill your suitcase with gold bars or $100 bills? Assume first that how much you can carry is a fixed weight. Then redo your analysis assuming that how much you can carry is a fixed volume. As I estimated in suitcase of money the mass of a paper note is about 1 gram, and the volume is about 1 cm³.

  • Edward Ross
Estimating Weight with Body Mass Index
insight

Estimating Weight with Body Mass Index

When estimating things it's good to find approximate constants, typically ratios, that are easier to remember than things that vary. The Body Mass Index (BMI) is an example for measuring people. It's relatively easy to measure human height, as a human. For example I'm about 180cm tall; the top of my nose is about 170cm, the bottom of my chin is about 160cm and the bottom of my neck is about 150cm.

  • Edward Ross
How much Money is in a Suitcase?
insight

How much Money is in a Suitcase?

This is from Sanjoy Mahajan's The Art of Insight Problem 1.3 In the movies, and perhaps in reality, cocaine and elections are bought with a suitcase of $100 bills. Estimate the dollar value in such a suitcase. Size of $100 note Let's assume a banknote is about the same thickness as paper; Australian notes are probably a little bit thicker. A 500 page ream of paper is about 5cm tall, so each sheet is about 0.

  • Edward Ross