My heroine has been stabbed - run through the abdomen by a foot-long dagger - and is bleeding to death. She is currently crawling toward her salvation through a very cold place. She is magically immune to the harmful effects of low temperatures, but her blood, once it has left her body, is not.
I wrote a passage stating that as she crawled on hands and knees, her blood was dripping from the point of the dagger that has impaled her, and the environment was so cold that the blood didn't splatter on the ground, but instead froze solid and bounced.
My heroine is for purposes of this question a perfectly proportioned human female 170cm tall, weighing 70kg. Despite the extremely cold environment, her body temperature is a normal 37°C. The point of the dagger is protruding from her abdomen so that it's point is level with the lowest point of her belly. She is crawling on hands and knees, with straight arms. While she has been stabbed, and major organs are involved, the continued presence of the dagger is acting as a plug, preventing a rapidly fatal loss of blood. Most of her loss of blood is going into her abdomen, but enough is leaking out around the point of the dagger that it is dripping rather than gushing. Gravity is a normal 9.8m/s^2, and atmospheric pressure is around 60kPa, about average for an altitude of a bit over 4000m ASL. Please assume that the temperature of the blood droplets start at 37°C, and cooling does not begin until the droplet is falling freely, and the droplets must be frozen completely solid before hitting the ground, which for purposes of this question is effectively a flat surface. The blood droplets have not begun to clot significantly.
So, my question is this: Just how cold would it have to be for human blood to freeze solid before hitting the ground, so that the frozen droplets would bounce rather than liquid blood splattering? Is the required temperature realistic, in that Nitrogen and Oxygen can remain gaseous, and/or the temperature above 0K, or must it be "Magically cold"?
I am looking for answers that include all necessary proof and calculations, hence the hard-science tag. I am not looking for educated guesses without a basis on fact. While I mention magic, magic is only involved perforce in setting the starting conditions, and the answer will be: Possible, Possible but x atmospheric gases would not remain gaseous at the required temperature, or Not Possible due to the required temperature being below 0K.
The droplets of blood will be falling a distance of approximately 30cm, though this may vary from 25-35 cm according to the exact position of the victim as she attempts to reach salvation. The blood droplets should therefore freeze solid after a downward journey of 25 cm at minimum.