I have also included a file for a pivot. If you insert a shaft through the wheel, you can use the pivots to mount it and make it spin. The wheel and pivots can be scaled to meet your needs.
Step 1: Circles
Make a second larger circle which will indicate the outer boundary of your spokes.
Step 3: Make a cut out
Convert it to an editable spline by right-clicking on it's name in the modifer tab.
Select the red "points" button.
Modify the shape of the egg to your liking. This will be the negative space between the spokes.
Step 4: Change pivot
Click on "Affect Pivot Only"
Click the rotation tool, and then change the Z-rotate option to 0.
Unclick "Affect Pivot Only"
Step 5: Create an array
Change the Z-rotate to roughly 40. If the copies appear to be touching, increase this number
Finally, increase the number of copies until they go all the way around your wheel.
Step 6: Attach
Right-click on the circle's name and make it an "Editable Spline"
Click the "Attach" button.
Next, click on all of the egg-shapes. As you click on them, they should change color.
Also, click on one of the inner, smaller, circles.
Step 7: Extrude
Set the amount of extrusion to be about a value of 1.