The big E is back! Sorry to hear of your setback enicalyth, my sincere wishes for a speedy accommodation of, and adaption to your new condition. If you feel disposed towards it, a post in the Medical section regarding the effects of and adaption to the mild stroke would be appreciated, it’s something that a lot of us may have to face one day.
Smells Like…, your question requires a dual answer, depending upon the condition. It depends upon whether you’re referring to the same aircraft at differing weights at either (1) the same speed, OR (2) the applicable aerodynamic performance speed, for example, Vmd.
If you consider a conventional drag curve, that is, Drag/Thrust required on the vertical axis, and Equivalent Airspeed on the horizontal axis, the drag curve for the heavier aircraft will move up, elongate, and move horizontally to the right.
Same Speed – The heavier aircraft at the SAME speed (e.g. 200 KEAS), will have to fly at a higher Angle of Attack AND body angle (important), to generate the increased lift required. The lift vector will therefore be greater, inclined more rearwards, with the horizontal component of drag increased by both the greater magnitude of the vector, and the higher trigonometrical vector due to the greater rearward inclination. That explains the increase in Induced Drag. As this higher angle of attack occurs at a higher body angle, the frontal area of the total airframe ‘facing’ the relative airflow is greater, thus a greater value of S (Surface Area) in the
Drag = Cd ˝ Rho V^2 S formula.
Thus, induced drag increases, as does profile drag to a generally lesser extent. Total Drag is greater.
Same aerodynamic performance speed (for example, Vmd) – Vmd and other aerodynamic performance speeds such as MRC generally occur at the SAME Angle of Attack, thus change in frontal area need not be considered. To produce the requisite lift at the same AoA, speed must be increased. The Total Lift vector will be at the same inclination for both aircraft, thus the trigonometrically derived rearwards factor is the same, but the magnitude is greater for the heavier aircraft, thus, Induced drag is greater. Frontal (profile) area will be the same for both aircraft, thus S may be taken out of the comparison, but as higher speed is required, the greater speed will lead to greater profile drag – V is the important determinant in the
Drag = Cd ˝ Rho V^2 S formula.
Again, Total Drag will be higher, and again, it all depends!!!!!
Caveats galore - Compressibility, transonic shock waves, kinematic viscosity etc. not considered.
Regards, and Happy New Year,
Old Smokey