[Paper Review] Added costs of insect-scale flapping flight in unsteady airflows

Dmitry Kolomenskiy, Sridhar Ravi+9 more|arXiv (Cornell University)|Oct 28, 2016

Biomimetic flight and propulsion mechanisms7 references3 citations

TL;DR

This study identifies that body roll in insect-scale flapping fliers due to unsteady airflow reorients the aerodynamic force vector, reducing vertical lift and increasing energetic costs. Using robotic and numerical models, it quantifies added mechanical power required to maintain altitude, showing increased flapping frequency and stroke amplitude as compensatory strategies with measurable energetic penalties in turbulent flows.

ABSTRACT

The aerial environment in the operating domain of small-scale natural and artificial flapping wing fliers is highly complex, unsteady and generally turbulent. Considering flapping flight in an unsteady wind environment with a periodically varying lateral velocity component, we show that body rotations experienced by flapping wing fliers result in the reorientation of the aerodynamic force vector that can render a substantial cumulative deficit in the vertical force. We derive quantitative estimates of the body roll amplitude and the related energetic requirements to maintain the weight support in free flight under such conditions. We conduct force measurements of a miniature hummingbird-inspired robotic flapper and numerical simulations of a bumblebee. In both cases, we demonstrate the loss of weight support due to body roll rotations. Using semi-restrained flight measurements, we demonstrate the increased power requirements to maintain altitude in unsteady winds, achieved by increasing the flapping frequency. Flapping fliers may increase their flapping frequency as well as the stroke amplitude to produce the required increase in aerodynamic force, both of these two types of compensatory control requiring additional energetic cost. We analyze the existing data from experiments on animals flying in von Kármán streets and find reasonable agreement with the proposed theoretical model.

Motivation & Objective

• To investigate how unsteady, time-periodic wind flows induce body roll in small-scale flapping fliers, leading to reduced vertical force production.
• To quantify the energetic cost of maintaining weight support when aerodynamic force vectors are reoriented due to body rotations.
• To evaluate compensatory flight control strategies—such as increased flapping frequency and stroke amplitude—used by fliers to counteract vertical force deficits.
• To validate theoretical models against experimental data from robotic flappers and numerical simulations of bumblebees.
• To compare theoretical predictions with published animal flight data in von Kármán wakes, assessing consistency with observed metabolic rates.

Proposed method

• Developed dimensionless parameters $Tu_w$ (turbulence intensity relative to flapping frequency) and $\theta_{vk}$ (body roll angle) to characterize unsteady flow effects.
• Conducted semi-restrained flight experiments with a miniature hummingbird-inspired robotic flapper to measure force and power under unsteady wind conditions.
• Performed high-fidelity numerical simulations of a bumblebee in unsteady flows to analyze body roll and force vector reorientation at insect scale.
• Derived theoretical relationships linking body roll amplitude to flow unsteadiness and flapping frequency, estimating added mechanical power requirements.
• Used dimensional analysis and scaling laws to generalize findings across flapping fliers, accounting for static and dynamic properties of the flapper.
• Validated theoretical predictions against published data on animal flight in von Kármán wakes, focusing on roll angle dependence on cylinder diameter, distance, and inflow velocity.

Experimental results

Research questions

• RQ1 How does time-periodic unsteady wind induce body roll in small-scale flapping fliers, and what is its impact on vertical force production?
• RQ2 What is the functional relationship between flow unsteadiness (characterized by $Tu_w$ and $\theta_{vk}$) and the resulting body roll amplitude?
• RQ3 What are the added mechanical power requirements to maintain altitude when body roll reorients the aerodynamic force vector?
• RQ4 How do compensatory control strategies—increased flapping frequency and stroke amplitude—affect energetic costs in unsteady flows?
• RQ5 To what extent do theoretical predictions of roll angle and power cost align with experimental data from animals flying in von Kármán wakes?

Key findings

• Body roll of up to 15° in bumblebees and 23° in hawkmoths during flight in unsteady wakes causes a measurable deficit in vertical force due to aerodynamic vector reorientation.
• In robotic flapper experiments, mean vertical force decreased by up to 12% when roll was permitted compared to fully tethered conditions under unsteady wind.
• The robotic flapper required higher input power to maintain altitude in unsteady winds, with flapping frequency increasing monotonically to compensate for roll-induced force loss.
• Numerical simulations of bumblebees showed that unsteady flows with frequencies below flapping frequency induce large body rotations, leading to significant vertical force deficits.
• Theoretical estimates of added mechanical power required to compensate for roll-induced force loss were consistent with reported increases in hummingbird metabolic rates during turbulent flight.
• The proposed model successfully predicted roll angle trends across varying cylinder diameters, distances from the cylinder, and inflow velocities in von Kármán wake experiments.