The lightweight cabs are hooked on to the horizontal beam, move on wheels via a motor and are designed to travel at up to 80km/h in urban areas and carry 4800 people an hour each way.
The system would be built above footpaths and roads, meaning no land would be bought or need to be developed. He included a map of how the network might look.
Chapman has patented the design in New Zealand, Australia, the US and Singapore.
When he saw there was to be a parliamentary inquiry into New Zealand's future transport needs, the architect saw it as an opportunity.
"It's getting drastic for Auckland. Ratepayers are being sucked for huge capital expenditure. We need something that will unclog the roads."
SkyCabs would halve journey times, reduce wait times to two minutes or less, were reliable, whisper-quiet and would increase the international reputation of Auckland.
He first submitted his plan to the former Auckland Council in 1998 and since then has had various meetings with officials but it has failed to gain traction.
"You would think if Auckland is choking with congestion the council would look at anything to help but it hasn't shown any interest."
Auckland Transport spokesman Mark Hannan said Chapman last contacted the council about three or four years ago but he hadn't been in touch since. He said he would be happy to meet.
Also among the submissions was one from Levitation Technologies, an Auckland company that wanted to introduce hoverboard technology, which it envisaged as playing a major role in transport.
The Transport and Industrial Relations Select Committee launched its inquiry into the country's future mobility in December.
It is investigating how changing transport technology and social and economic trends can enhance productivity in the economy, reduce transport costs and optimise transport infrastructure.
Submissions closed on April 1.