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How many projects can a project manager manage?  How do I quantify how many project a project manager should be able to manage?

In the past, I would give someone more projects until they couldn't keep everything on schedule from O3 to O3.  This worked as long as O3's were running well and priorities were in sync.  Unfortunately it is not useful for forecasting - nor is it quantified - everyone can say my projects are more complicated.  

Now, I am trying to do some staffing projections based on how many projects an average project manager can handle.  I am also trying to establish a baseline metric for the workload a PM of a certain level should be able to handle.  This needs to includes variables such as the size and complication of various projects.  

I should mention I work for a quasi-governmental agency, so I know exactly what projects are coming my way for the next two years and have a fairly accurate list for the next ten years.  We are a very project-centric organization that designs and constructs infrastructure projects.  Project managers in my branch manage design projects with fees that range from $300k to $3M.  Most designs last a year (duration varies more by number of agencies involved than by size).  As a government organization we replace revenue and profit metrics with cost and don't have goals for growth.  

Obviously it takes more work to manage the design team on a $3M project than it does for a $500k design project.  Considering standard project management protocols (scope, schedule, budget, quality, risk, etc etc etc) multiple small projects is also a challenge.  I am also finding a wide range in the average number of projects per project manager depending on the supervisor (even though the projects are all similar).  

Any thoughts on a way to quantify how many project a project manager should be able to manage?