Back in mid-century America, you did old-style sit-ups, which were once regarded as the gold standard of iron-gut, military discipline. Maybe they still are, so if your idea of "manly" is messing up your lower back, go for it. But few fitness trainers recommend old-style sit-ups, though there are some re-conceptualized versions of them that might work for you.
While the focus of Pilates is strength training, you'll get some cardio in with moves like this. Stand with your belly pulled in and your arms overhead. Inhale and lower your head, bending the knees and swinging the arms back. Exhale and jump up with straight legs, reaching the arms overhead. Land with the knees slightly bent and return quickly to starting position. Do 8-10 reps at a rapid pace. You should be out of breath when you finish.
Jump up ^ Lees C, Hopkins J (2013). "Effect of aerobic exercise on cognition, academic achievement, and psychosocial function in children: a systematic review of randomized control trials". Prev Chronic Dis. 10: E174. doi:10.5888/pcd10.130010. PMC 3809922. PMID 24157077. This omission is relevant, given the evidence that aerobic-based physical activity generates structural changes in the brain, such as neurogenesis, angiogenesis, increased hippocampal volume, and connectivity (12,13). In children, a positive relationship between aerobic fitness, hippocampal volume, and memory has been found (12,13). ... Mental health outcomes included reduced depression and increased self-esteem, although no change was found in anxiety levels (18). ... This systematic review of the literature found that [aerobic physical activity (APA)] is positively associated with cognition, academic achievement, behavior, and psychosocial functioning outcomes. Importantly, Shephard also showed that curriculum time reassigned to APA still results in a measurable, albeit small, improvement in academic performance (24).  ... The actual aerobic-based activity does not appear to be a major factor; interventions used many different types of APA and found similar associations. In positive association studies, intensity of the aerobic activity was moderate to vigorous. The amount of time spent in APA varied significantly between studies; however, even as little as 45 minutes per week appeared to have a benefit.

The aim of this study was to assess the effects of vigorous exercise on functional abilities by means of a Senior Fitness Test (SFT) in a group of elderly adults. Twenty healthy and inactive people performed vigorous exercise (VE: 12 men and 8 women, aged 69.6 ± 3.9 years). At the beginning of the study (T0) and after 3 months (T1), each subject's functional ability was tested for muscular strength, agility, cardiovascular fitness, flexibility, and balance. The VE was designed with continuous and interval exercise involving large muscle activities. Functional exercises were performed between 60% and 84% of heart rate reserve (HRR) for a duration of 65 minutes. Five out of the 6 SFTs performed were found significantly improved: Chair Stand (T0 12.4 ± 2.4, T1 13.5 ± 2.6, p < 0.01), Arm Curl (T0 14.2 ± 3.6, T1 16.6 ± 3.6, p < 0.01), 2 min step (T0 98.2 ± 15.7, T1 108.9 ± 16.2, p < 0.01), Chair Sit-and-Reach (T0 −9.9 ± 7.7 cm, T1 1.7 ± 6.3 cm, p < 0.01), and Back Scratch (T0 −15.8 ± 10.9 cm, T1 −8.4 ± 13.1 cm, p < 0.01). Our results suggest that a high intensity protocol and functional exercises can improve functional mobility and muscle endurance in those over 65 years of age. SFTs are an effective method for assessing improvements in the functional capacity of elderly adults.
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