# How far can an Aarakocra Totem Warrior Barbarian get a grappled target with flying?

Friend of mine picked an Aarakocra Barbarian as his new character, with the Path of the Totem Warrior selected. He's level 7, and has taken Eagle as his level 3 "Totem Spirit", and Bear as his level 6 "Totem Spirit".

Eagle. While you're raging and aren't wearing heavy armor, other creatures have disadvantage on opportunity attack rolls against you, and you can use the dash action as a bonus action on your turn.

Bear. You gain the might of a bear. Your carrying capacity (including maximum load and maximum lift) is doubled and you have advantage on strength checks made to push, pull, lift, or break objects.

PHB, pg. 50.

With this in mind, how much speed does this character have while grappling a target of medium size? Can they do it to large as well considering the new bonuses?

Here's my logic. Carrying capacity = STR x 15. Our Barbarian's STR = 16 (16x15 = 240, which is the weight in pounds it can carry).

With 240lbs doubled (Bear Totem) to 480lbs, that is just about the maximum weight a "medium" creature can weigh (500lbs max, 5th Edition SRD).

Does this cause the Aarakocra to be able to move its full 50 ft. with a medium sized target? or does it fall victim to the half restriction that "Carrying or Lifting" applies, where it could only move 25 ft.

Two scenarios exist in my mind:

1. Aarakocra grapples a medium target, flies 25ft into the air, bonus action "Dash" for 25ft more, and either drops the target (50ft = 5d6 bludgeoning dmg), or waits for the next turn to fly higher (50ft more, for 100ft total, or 10d6)

2. Aarakocra grapples a medium target, flies 50ft into the air, bonus action "Dash" for 50ft more, and either drops the target (100ft = 10d6 bludgeoning dmg), or waits for the next turn to fly higher (100ft more, for 200ft total, or 20d6)

Do I have this correct?

Edit Clarification: Does anything I have listed remove the -halved- movement speed restriction for flying a grappled target greater than 2 sizes smaller than you?