The only problem I see with your idea and I`m not knocking it or saying it won`t work is not having a membership fee.
These gyms have done a massive study over the years and the reason they charge membership fees is the fact that they have to make budget every month. Such things as rent, light bill, water, sewer, trash, cable t.v. and insurance. Most gyms also know that most people sign up after the first of the year when they have made those promisess to get back into shape. The problem comes when people decide after a month or so that they don`t have time this week to make it to the gym, then it turns into 2 weeks then a month and so on. With them haveing the membership already payed for they know they can make those monthly payments even if the customers do not show up.
Your idea of no membership leaves a big void. What happens if during the summer most of your customers are gone on vaccation? How do you make those monthly payments? What happens during the winter if you live in an area that has heavy snow fall and people can`t get to your for a week or two?
I would think the first step would be to sit down and write a serous business plan and marketing plan. Make sure if your classes fall off that you can make your budget each month. Those plans should show your strong and week points.