'Caught by suprise' or just sloppy sums?

A recent Age article contains a claim attributed to the Minister for transport that 'a rise in train patronage had caught the Government by surprise'.

'It has been over 18 per cent in the past two years, which is massive," she said. "We usually operate on the basis of 3 to 4 per cent increase since we have come to office.'

The government has also claimed a policy of achieving 20% modal share for public transport by 2020. Since modal share is currently around 10% it follows that a dramatic increase in patronage is needed to achieve the modal share aim. Assuming no population increase and no increase in motor vehicle trips per capita, a doubling would be necessary. With population growth and car usage per capita still increasing, the actual increase would need to be more - perhaps around 150%.

Let us assume that we have, in 2007, a city of 100 people. It makes 1000 motorised trips per annum per capita of which 100 by public transport (ie a 10% modal share). Doubling modal share would require a shift of 100 trips to public transport from some other motorised mode. So that makes 200 trips, assuming that there is no change in the volume of travel per capita.

Then there's population growth. Assuming 1.4% pa growth rate this would take us to 120 people by 2020. Perhaps 1.4% pa is a bit higher than the historical record, but note that the population is ageing and the number of people of driving age is increasing faster than the general growth rate.

Thus the total number of public transport trips would need to increase from 100 people x 100 trips (10 000) to 120 people x 200 trips (24 000) per annum to meet the target. That earlier 150% estimate is pretty close.

Compound percentages are tedious to calculate, but financial people do it every day and have developed handy calculators such as this. Luckily they are just as good for other uses such as passenger growth calculations.

For our purposes, we have an ending value of 24 000 and a starting value of 10 000. It's 13 years until 2020, so the number of periods is 13. This produces a required compound annual percentage growth of 6.97%. As it doesn't allow for driving growth, it understates the growth required, which in practice would be in the 7-8% pa region.

Of course this is an average across all modes. But given likely continued suburban development, one would expect that growth of trains and buses would need to be well above 7% while trams could grow slower (these generally only serving established inner suburbs and no major tram extensions planned).

To achieve 20%/2020 an average annual patronage growth of at least 7% is required. If the government banks on 3-4% growth then it can kiss the 20% by 2020 aim goodbye as the numbers don't stack up. Furthermore the annual growth requirements get more onerous and eventually almost impossible the later it's left.