A hydrocarbon well drilling system comprising: a wellhead system comprising a wellhead body disposed at a surface of the earth, characterized in that the wellhead body comprises a wellhead passage configured to guide a drill string from a horizontal orientation to a downward sloping orientation of a wellbore having a sigmoid well trajectory, the wellhead passage extending from a wellhead entrance at a vertically oriented side of the wellhead body to a wellhead exit at a horizontally oriented underside of the wellhead body; the drill string configured to pass through the wellhead passage, the drill string comprising a horizontally oriented starting end and a drill bit configured to bore through a subsurface formation to create the wellbore having the sigmoid well trajectory, the wellbore comprising: a first sigmoid portion extending from the wellhead exit to an inflection point of the wellbore, the inflection point being located downhole from the wellhead exit, the first sigmoid portion of the wellbore comprising a first trajectory that is generally horizontal at the wellhead exit of the wellbore and that increases in slope to a first gradient at the inflection point; and a second sigmoid portion extending from the inflection point of the wellbore to a transition point of the wellbore, the transition point being located downhole from the inflection point, the second sigmoid portion of the wellbore comprising a second trajectory that matches the first gradient of the first sigmoid portion of the wellbore at the inflection point and that decreases in slope to a second gradient at the transition point; and a drilling control system, comprising: a motive system configured to exert a horizontal motive force on the horizontally oriented starting end of the drill string to generate a force to facilitate the drill bit boring through the subsurface formation to create the wellbore having the sigmoid well trajectory. a wellhead system comprising a wellhead body disposed at a surface of the earth, characterized in that the wellhead body comprises a wellhead passage configured to guide a drill string from a horizontal orientation to a downward sloping orientation of a wellbore having a sigmoid well trajectory, the wellhead passage extending from a wellhead entrance at a vertically oriented side of the wellhead body to a wellhead exit at a horizontally oriented underside of the wellhead body; the drill string configured to pass through the wellhead passage, the drill string comprising a horizontally oriented starting end and a drill bit configured to bore through a subsurface formation to create the wellbore having the sigmoid well trajectory, the wellbore comprising: a first sigmoid portion extending from the wellhead exit to an inflection point of the wellbore, the inflection point being located downhole from the wellhead exit, the first sigmoid portion of the wellbore comprising a first trajectory that is generally horizontal at the wellhead exit of the wellbore and that increases in slope to a first gradient at the inflection point; and a second sigmoid portion extending from the inflection point of the wellbore to a transition point of the wellbore, the transition point being located downhole from the inflection point, the second sigmoid portion of the wellbore comprising a second trajectory that matches the first gradient of the first sigmoid portion of the wellbore at the inflection point and that decreases in slope to a second gradient at the transition point; and a first sigmoid portion extending from the wellhead exit to an inflection point of the wellbore, the inflection point being located downhole from the wellhead exit, the first sigmoid portion of the wellbore comprising a first trajectory that is generally horizontal at the wellhead exit of the wellbore and that increases in slope to a first gradient at the inflection point; and a second sigmoid portion extending from the inflection point of the wellbore to a transition point of the wellbore, the transition point being located downhole from the inflection point, the second sigmoid portion of the wellbore comprising a second trajectory that matches the first gradient of the first sigmoid portion of the wellbore at the inflection point and that decreases in slope to a second gradient at the transition point; and a drilling control system, comprising: a motive system configured to exert a horizontal motive force on the horizontally oriented starting end of the drill string to generate a force to facilitate the drill bit boring through the subsurface formation to create the wellbore having the sigmoid well trajectory.