Help me with my Higher rate pension tax relief sums please?

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I earn £70,000 gross a year which I calculate to mean I will pay £11,046.00 higher rate tax this year.
I plan to start a pension this year and thought I would maximise the investment by maximising the high rate relief I can receive.
Am I right in thinking I should invest £27615 in order to get £11,046.00 in tax rebated?
I think this means I really invest £22,096 into the pension which receives an instant boost of 20% (£5525) and I then claim a further (£5525) as relief using a self assessment tax form?
If this is the case I will do the same thing again in April 2016 for the following tax year.

Are my sums correct?
Is there a way to do it without being stuck filling out a self assessment tax form each year?

Thanks for your help!

[LozaACCS]

Yes it is correct.
You could consider agreeing a salary sacrifice arrangement with your employer in return for an ER contribution to your scheme, they could operate relief at source through the PAYE regime, this would avoid the need to complete a tax return.