Aldarion
Archmage
Stronger character would not help, because he would probably just bury himself into the ground trying to bowser toss something that size.So in theory, we either need a smaller dragon or a stronger character for this to work with 'real' physics.
So you need to calculate pressure that tossing something size of Smaug would create. For reference, movie Smaug is 130 meters long... 9 metre anaconda can weight up to 250 kg, while saltwater crocodile can be up to 5 meters and 1 100 kg. So Smaug, being considerably larger and far less snake like, would weight a minimum of 753 metric tons (anaconda) and a maximum of 19 333 metric tons. Average human feet have surface area of 100 cm2. This results in static pressure of anywhere between 75 300 000 kg / m2 and 1 933 300 000 kg / m2, or from 738 to 18 959 MPa. For comparison, compressive strength of steel is some 1500 MPa, while medium ground has compressive strength of anywhere between 10 000 to 30 000 psi or 69 to 207 MPa.
Basically, your character will punch himself into the earth, Wile E Coyote style.
But as stated, bowser toss is a toss. This means acceleration, which means dynamic pressure. Now, I am no physicist and I kinda suck at physics... but in order to produce centrifugal force for a toss, you need to overcome gravity. Thus centripetal acceleration has to be above 9,81 m/s^2. From this, tension force is (m*v^2) / r. Using radius of 70 meters (Smaug's center of mass, let's say) and this, we need tangential velocity of 26 m/s. This means centripetal force of anywhere between 7 831 200 and 201 063 200 Newtons. This results in pressure of between 783 120 000 and 20 106 320 000 Newtons per square meter, or 783,12 to 20 106 MPa.
So yeah. No tossing dragons around unless you are standing on a neutron star. And in that case, I suggest you have a little bit more pressing issue than trying to figure out how to toss a dragon around.
Hope I didn't screw anything up... this was fun, but I hadn't done any actual physics calculations in last ten years or so.